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When you have a ratio problem, you can always think of it like this:
The ratio of cars to vans is 8 to 1. Just think of that as 8x to 1x.
If the TOTAL number of cars and vans is 189, just take the info above and set up the equation like this:
8x + 1x = 189 (equation)
9x = 189 (add the like terms together)
x = 21 (divide both sides by 9 to isolate the x)
Now you know that x equals 1. Plug that into your ratios like this:
CARS
8x
8(21) = 168
VANS
1x
1(21) = 21
That means there are 168 cars and 21 vans. You can check that like this:
168 cars + 21 vans = 189 cars and vans total.
I hope this helps. :-)

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2(p + 4) = 7p + 2 <---- original problem
2p + 8 = 7p + 2 <---- distributed the 2 to "p" and to "4"
-7p ..... -7p <---- subtracted 7p from both sides of the equation
____________________
-5p + 8 = 2
..... -8 .... -8 <---- subtracted 8 from both sides of the equation
____________________
-5p = -6
= <----divide both sides by -5 to isolate the 'p'
p =
Does this work? We can plug in the answer into "p" in the original problem.
2(p + 4) = 7p + 2
2() = 7 + 2
+ 8 = + 2
+ = +
=
Now we can see that yes, the solution works. :-)

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ivide
(42b^3+23b^2+32b+41) divided by (6b+5)
not sure which is the ans. if at all correct.. i am so confused
7b^2-2b-7-6/6b+5 or 7b^2-2b+7+6/6b+5



These are confusing but don't panic. These are not impossible. Here is your problem:



My problem in showing this to you is going to be how to make this show up in typing! Arrgghh. I'm going to use this as my dividing sign: ]

I will also draw a line above that symbol, so I can TRY to make this division look normal! It will look like this:

.________________________
]


So here goes:
......._________________________
]
.........
________________________
...................
...................
_____________________________________
..............................
.............................
____________________________________________
.....................................


Therefore... our answer is:

I'm sure this looks weird to you. If I could scan a copy of my work to you, it would be easier for you to see! I'm sorry it doesn't show up well here but maybe you can see thru how awful this looks and it will make sense to you.

Good luck and I hope this was helpful. :-)

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Find the dimensions of a rectangle with a perimeter of 112 cm if the length is 4 cm less than four times the width.


Ok... you have to first tell yourself that a perimeter is the sum of the measurements of all four sides of the rectangle. In other words, you add all four sides and voila, you have the perimeter.

In a rectangle, tho, you have TWO lengths and TWO widths. The equation to find the perimeter, then,if we use "L" for Length and "W" for Width is:

L + L + W + W = Perimeter

Now this problem tells us that the perimeter is 112 cm. At first then, we can set up this equation: L + L + W + W = 112. We don't know, tho, the lengths and the widths - or do we?

WELL.. the problem says this: the length is 4 cm less than four times the width. All you have to do is write that information in an equation form. Break down what you are given and see what you come up with:


The Length: L
is: =
4 cm less than 4 times the width: 4w - 4 <---See how this is 4 cm less than four times the width?

Our equation then is: L = 4w - 4 and you can PLUG this info into the equation we started with, like this:

L + L + W + W = 112
4w - 4 + 4w - 4 + W + W = 112 (see where I replaced "L" with 4w - 4? Now combine like terms, by adding the "Ws" and the numbers:

10W - 8 = 112 (now add 8 to both sides to start to isolate the w)
10W = 112 + 8
10w = 120 (now divide both sides by 10 to further isolate the w)
w = 12


SO --- now we know that w = 12. We can just plug this info into what we were told about the length, which was: the length is 4 cm less than four times the width OR as we wrote it: L = 4w - 4

SO let's use that equation and plug in our info:

L = 4w - 4
L = 4(12) - 4 (See where we plugged "12" in where the "w" was?)
L = 48 - 4
L = 44

Now we know that the width is 12 and the length is 44. Does that work out in what we know to be the perimeter of the shape? We were told the perimeter was 112 cms, so, let's test our numbers out:

L + L + W + W = 112
44 + 44 + 12 + 12 = 112

YAY! It works out! Sooooo our length is 44 cm and our width is 12 cm.

I hope this was helpful. :-)

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4+6x>4x-18

Solve this like you would solve the problem if there were an equal sign in the problem. Put your "Xs" on one side of the equation and your numbers on the other side......

4 + 6x > 4x - 18 (original equation)
4 + 6x - 4x > 18 (subtract 4x from both sides of the equation)
4 + 2x > 18 (6x - 4x = 2x)
2x > 18 - 4 (subtract 4 from both sides of the equation)
2x > 14 (18 - 4 = 14)
x > 7 (divide both sides by 2 to isolate the 'x')

If you graph this, you draw a number line with a circle around the 7 (you don't fill in the circle) and thennnn you draw an arrow from that circle that goes to the right.

I hope this is helpful. :-)

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Evaluate the variable expression when .a=-1/4, b=7/8, and c=1/8
8a + (7b -c)


Just "plug" in the info you are given, like this:

a =
b =
c =

8a + (7b - c) (original equation)
8 + ( - ) (see where the fractions are substituted in for the variables?)
+ (If you multiply 8 times you will get and... If you multiply 7 times you will get )
(If you subtract: you get: )
(Reduce the fractions: and )
(if you take -2 + 6 you will get 4)

I hope this helps you. :-)

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/

Factoring is tricky but don't let it intimidate you. Just do this:



Now can you see that these highlighted terms cancel each other?


BUT when I say: "cancel" I'm not meaning that you can just just wipe out the (x + 4) in the numerator. Why? Well, when we "cancel" terms, we aren't just DELETING them! Think of this: = 1, right? Similarly, = 1, right?


SO when we cancel out the (x + 4) above, we are really saying that equals 1.


Therefore, this:

is really:

Does that make sense? I hope so. If you need more help with canceling and factoring, check out my YouTube videos. Just do a search on YouTube for PRMathChicago and when you find my name, you'll see some vids that my help you because they explain this in more detail.

Good luck. :-)

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First you have to factor the numerator and the denominator, like this:




Now look at this:



See how those two highlighted terms can cancel each other out? Then you are left with your answer, which is:



I hope this is helpful but for more examples of this type of problem, check out my YouTube videos. Just do a search on YouTube for PRMathChicago. When you find my name, there are a few videos there that show and explain this type of work in more detail.

Good luck! :-)

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x-intercept and y-intercept of the line 2x+3y=-18

Here are two facts to keep in mind:

When you want to find the X intercept SOLVE for X by making y = 0
When you want to find the Y intercept SOLVE for Y by making x = 0.

It's that simple. Just plug in 0... like this:

Let's find the X intercept first. We'll SOLVE FOR X by making y = 0.

2x+3y=-18 (original equation)
2x + 3(0) = -18 (plug in 0 for the y variable)
2x = -18 (3 times 0 equals 0, so we just wipe it out of the equation).
x = -9 (Divide both sides by 2 to isolate the x. So, -18 divided by 2 is -9)

Now we know, when y =0, then x = -9. So our X intercept is: (-9, 0)


Now let's find the Y intercept. We'll SOLVE FOR Y by making x = 0.
2x+3y=-18 (original equation)
2(0) + 3y = -18 (plug in 0 for the X variable)
3y = -18 (2 times 0 equals 0, so we just wipe it out of the equation).
y = -6 (Divide both sides by 3 to isolate the y. So.. -18 divided by 3 is -6)

Now we know, when x = 0, then y = -6. So our Y intercept is: (0, -6)

That's all there is to it. I hope this was helpful. :-)

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Grace has 16 jellybeans in her pocket. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
I know the answer is 13 but I don't even know where to begin. It doesn't make any sense.


This isn't so much a problem of a math equation, but instead of logic. I hope I explain this well for you. Think of this..............

You have 8 red jellybeans, 4 green and 4 blue. If you held these beans in a bag and took out just 8 jellybeans, it is entirely possible that you could pull out 8 RED ones. (It would be pretty unlikely you would pull 8 red ones out, but it is definitely possible!) Sooooo... ok... now you have pulled out 8 red jellybeans. Keep the number 8 in your mind.

Now there are 4 green and 4 blue left, right? If you took FOUR more beans out of the bag, it is entirely possible that you could pull out 4 green ones. This is unlikely to happen but again, it is definitely possible! So now you have 8 red ones and four green ones. That's 12 beans in all and you STILL don't have one of every color.

What's left in the bag? You have 4 blue left. If you pull out ONE more bean, you will then have one jelly bean of each color. You had 12 beans and now this final bean means you have a total of 13 jellybeans.

THAT'S why it takes 13 beans to be ABSOLUTELY sure you have one of each color.

I hope this makes sense for you. :-)

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Which answer choice is the set of all solutions to the inequality |x + 3| > -2?

A. There are no solutions.
B. x < -5 or x > -1
C. x > -5 and x < -1
D. All real numbers.

With all respect to the person who has already answered this problem, I am sorry to say that I think that person is wrong. The answer to this problem is A: There is NO solutions.

Why?

The absolute-value principle reminds us that absolute value is always non negative.

Therefore,your equation of: |x + 3| > -2 has no solution, which is "A" in your choices.

I hope this helps you. :-)

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Solve the formula for v: g = f – v

This is very similar to your other problem, so let's solve it by asking the question of: How can we isolate the "v"?

Well, what is going on with the "v"? You can see that an "f" is added to the "v" so how about we do the OPPOSITE of adding an "f"? Let's SUBTRACT "f" from the equation and of course, we have to do this on both sides of the equation.

Therefore, we have:

g = f - v (Original equation)
g - f = f - f - v (Subtract "f" from both sides of the equation).
g - f = -v

You are still not done. Why? Well, the "v" is still not isolated! There is a negative sign in front of the "v", which means that there is a -1 next to the "v". You see, in front of any variable, there is always a "1" next to the variable and in this case, that 1 happens to be a NEGATIVE 1.

How do we isolate the "v"? How can we get rid of that negative 1? How about if we DIVIDE by -1? AND of course, we have to do this on both sides of the equation:

g - f = -1v

= See how the -1 cancels out?

So now you have: v = which is also:

v = -g + f

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Solve the formula for f: g = f – v

When solving for a variable, ask yourself: How can I isolate the variable?

In this problem, you ask: How can I isolate the "f"? Well... what is going on near the "f"? You can see that there is a "v" that is subtracted from the "f". So... to isolate the "f", let's get rid of that "v". How?

Well, you are subtracting "v" so let's do the opposite: Let's ADD "v" to the equation and if we do it on the right side, we must also do it on the left. Therefore, you have this:

g= f - v (Original equation)
g + v = f - v + v (Add "v" to both sides of the equation)
g + v = f (-v + v = 0, (so to speak) and so, our "f" is now isolated).

THEREFORE: f = g + v

I hope this helps. :-)

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You were already given an answer to this problem, but I think the tutor accidentally hit the number 9 on his puter, instead of "0".


Let's review: The previous tutor said that if you put y = 9 into the y = mx + b format, you'd get: y = 0x + 9. AND since "m" represents the slope, you can see that the slope in this case, is a 0. (The previous tutor said the slope was 9 -- and that's a typing mistake, I'm certain).

Let's discuss slopes in general:

When x equals a number, it is a VERTICAL line and the slope is UNDEFINED.

When y equals a number, then you have a HORIZONTAL line and the slope is 0.

I tell students that the way to remember that horizontal lines have a slope of zero is to think that the word "HORIZONTAL" has two letter Os in it. I say that those Os are actually zeros, reminding you that horizontal lines have 0 as a slope. :-) Ok, corny but it works.

Good luck with your math and I hope this helps you. :-)

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Do you change the sign when dividing by an negative or do you do it before?

This is a confusing question, because I'm not sure the type of problem you are referring to, given that there are many instances where you divide by a negative.

For example, consider these rules:
A positive divided by a negative is a negative.
A negative divided by a negative is a positive.

In those cases, you are changing the sign.

If you are talking about inequalities, then you "flip" the sign when you divide by a negative.

For example, you could solve for "X" in the problem below, and you'd have to flip the sign because you are dividing by a negative. See the following:

-2x < 6
x > -3 (see how the sign flipped when we divided by -2? And see how the answer became -3 because we divided a positive by a negative?)

Here's another example:
-3y > -9
y < 3 (Again, the sign flipped because we divided by a negative. BUT, -9 divided by -3 gives a +3, so the answer was positive, which is also a changed sign).

If you give a sample question, you may get a little more help. I hope this helps you tho. :-)

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PV = nRT; T
Hi Lauren...

When you solve for any variable, always think of "undoing" whatever operation is going on, so that you can get the variable all by itself. What do I mean? Well, if you are multiplying, for example, how to you "undo" that? You can divide. In another example, if you are adding, you can "undo" the adding by subtracting. Do you get the idea?

Soooo in your equation, you have PV = nRT and you have to solve for T. SO to get "T" all by itself, ask yourself, what is going on in the equation between "T" and nR? As you can see, the variables nRT are being MULTIPLIED together. How can we "undo" multiplication? We can DIVIDE.

We can DIVIDE nR away from T, BUT if we do it on one side of the equation, we have to do it on the other so PV must be divided by nR, also.


SO.... let's just DIVIDE nR on both sides of the equation, like this:


PV = nRT (original equation)

= Now nR is divided from both sides of the equation. Ok... can you see what I have highlighted? These highlighted terms can cancel each other out, like this:

=

Then what do you have left?

You have:

= T

That's all there is to it. Just identify what is going on with your variables, and try to "undo" whatever operation is performed, so that you can work to get your variable by itself.

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Think of a cylinder like a can of pop, k?
At the top of the can, there is a circle. At the bottom of the can, there is a circle. Now if you cut off the top and you cut off the bottom and sort of spread out the can (uncurled it), you'd have a rectangle.

Now picture this:
The height of the rectangle is the height of the can. Can you picture that?
The top of the rectangle is REALLY the the circumference of the circle. How so? Think about it -- it was a circle until you uncurled it. So the measure of the circumference of the can will not change simply because you uncurled it, right?

Sooooo to get the total surface area of the cylinder, you use this equation:

FIRST find the "lateral area" (the rectangle) which is:
r is the radius
h is the height

NEXT find the areas of two bases (the top and bottom of the can). The area formula for ONE circle is: Area =
r is the radius.

HOWEVER -- there are TWO circles (the TOP and the BOTTOM of the can) soooo, we have to find the TWO bases so our formula for the TWO bases is:


IF we add the lateral area plus the base areas, we'll know the total surface area.


Our final equation is:

Total Area of a Cylinder = +

Just put in the correct numbers for the radius and height and do the math and voila - you'll have the total surface area.

If you need more help, just get a specific question (such as the measurements of a sample problem) and post it here. I'm sure someone can give you more info if you need it.

I hope this helps. :-)

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When you want to find the "X" intercept, then solve for "X" by making Y = 0

When you want to find the "Y" intercept, then solve for "Y" by making X = 0.

Now that you know those two facts above, let's solve for the "X" intercept first. The "X" intercept means we solve for "X" by making Y = 0.

Here's your equation:
-4x + y = -4 Now let's plug in 0 for the Y variable and solve for "X"
-4x + 0 = -4
-4x = -4 (Now let's divide by -4 to isolate the "X")

=
x = 1

SO X = 1 when Y = 0. Our ordered pair would be: (1, 0)


Now let's do the "Y" Intercept. The "Y" intercept means we solve for "Y" by making "X" = 0

-4x + y = -4 Now let's plug in 0 for the X variable and solve for "Y"
-4(0) + y = -4 See where the 0 is in place of the "X" variable?
0 + y = -4 If you multiply -4 times 0, you will get 0.
y = -4
SO... Y = -4 when X = 0. Our ordered pair will be: (0, -4)

I hope this helps you. :-)

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What is the square root of 5 on the outside of the check mark and 18 inside the check mark?

(I love the description of the square root sign as a check mark. That was a great description and let me know immediately what the problem should look like). :-) Excellent. :-)

So ok... here is your problem:

Think of the various ways you can reach 18 through multiplication. There is:




Let's look at that choice. In that situation, you can take the square root of 9, right? In other words, you know what this is: . This answer to is 3. Keep that in your mind now and look at your problem this way:

<----This can be rewritten as:


Now... let's take the square root of 9, which is 3, k? We can "pull" that 3 out of the square root sign and we'll leave the 2 on the inside of the square root sign -- inside the check mark, like this:

BUT don't forget the 3 that you got from the . You have to multiply that 3 times the 5 that was already sitting outside the sign.

soooo we write the problem as:

So... here it is so you can see it all together:






I hope this helps. :-)

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1. One leg of a right triangle is 2 feet longer than the other leg. The hypotenuse is 10 feet long. Find the length of the legs of the triangle?

One leg of the right triangle is unknown: We'll call it "x"
The other leg is 2 feet longer than the other leg: 2 + x
The hypotenuse is 10 feet long.
You know ("c" is the hypotenuse). Now let's fill in the blank.

Now let's fill in what we know.
One leg is "x"
The other leg: 2 + x
The hypot. is: 10



(FOILED the above)

(subtracted 100 from both sides of the equation)
(combined like terms)
(factored out a 2 from everything)
(divided 2 from both sides of the equation)
= 0
x = -8 or x = 6 (disregard the -8 because a side cannot equal -8)

Does this work? If one side is 6 and the other is 2 more than 6 (or 8) and the hypotenuse is 10, then we have:


} YAY it works.


2. One leg of the right triangle is 5 units. The hypotenuse is one unit longer than the other leg. What is the length of the hypotenuse and the other leg?

One leg is 5 units: 5
The hypotenuse is 1 longer than the other leg: X+ 1
The other leg is: X

Put it all together:









Does x = 12 work?

One leg is 5
The other is 12
the hypotenuse is one more than 12: this is 13



YAY this works, too.

I hope this helps you.

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When you are multiplying with exponents, if the bases are the same, then you ADD the exponents. In this case, you have the same base, which is 4. Therefore, you just add the exponent 5 with the exponent 7.

You get this:
=


I hope this helps. :-)

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Ok, first you have to factor the numerator, which will be:



Now you have this for your problem:




See what I have highlighted? These can cancel each other out, like this:



When you cancel those terms, you get the answer:

If you search for PRMathChicago on YouTube, you'll see more examples of rational expressions like this. Maybe something there will help you.

I hope this helps. :-)

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x = 4 is a VERTICAL line. All vertical lines have an UNDEFINED slope.


If it had been y = 4, then you would have had a horizontal line, and horizontal lines have a slope of ZERO.

I hope this helps.

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How would we find the distance between a pair of points?
Our numbers are
(5, -1) and
(-2,3)
Please please help!!! I am so so so confused!!!


Math can be very confusing. Try not to worry - this is not too hard. Here's what you have to know:

Your points are:
(5, -1) and (-2, 3)

Ok, the first set of points are (5, -1) and so the 5 is the "x" and the -1 is the "y". Since there are TWO sets of points, let's label this FIRST set as:

5 =
-1 =
The second set of points are (-2, 3) and so, the -2 is the "x" and the 3 is the "y". Now let's label this SECOND set of points this way:

-2 =
3 =

Now let's fill in your formula. The distance formula is:



We just have to fill in what we know, k?
Remember this info:

5 =
-1 =

-2 =
3 =

Now just fill in the info:

Distance Formula
All the "x" and "y" info is plugged in. and
Now think: and


etc You can round this to: 8.06

Do you see how you just have to identify your first and second set of ordered pairs. Then you just plug that info into the formula and solve it. Not too scary after all, right?

I hope this helps you. :-)

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You have to give more information than that. What are you asked to prove? What is the shape of the figure you have to write a proof about? If you type the problem up thoroughly, then you can get help here definitely.

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Juan left home on his bicycle at 10:00 a.m. traveling at 21 km/h. At noon, his brother set out after him on his motorcycle following the same route. If the motorcycle traveled at 63 km/h, what time did Juan's brother overtake him?
Thank you, sir

You just need to think of the importance of this equation:

In other words, RATE times TIME equals DISTANCE.

Now....with that info, make a little chart for yourself:

________RATE_______TIME______DISTANCE_________
Juan..............21.........................T............................D............
Brother........63.........................T -2......................D............


See, the brother started out two hours behind Juan, or T - 2.

Also, when the brother overtakes Juan, then that means they will be at the exact same place, or the exact distance from the starting point. In other words: The distance for Juan equals the distance for the Brother.

Knowing that they have to be at the same distance means that you set up an
equation of: Distance = Distance (Or D = D)


SO... let's say:
D = D What does "D" equal?

"D" equals RATE times TIME.
For Juan, the RATE times TIME is: 21(T).
For the brother the RATE times TIME is 63(T - 2)

Let's fill in that info:

D = D
21(T) = 63(T - 2) Now let's distribute the 63 to the T and 63 to the -2.
21T = 63T - 126 Now let's subtract 63T from both sides to get the T variables on one side.
21T - 63T = -126 Now let's subtract: 21T - 63T which is: -42T
-42T = -126 Now divide both sides by -42 to further isolate the T.
T = 3

Now if T equals 3 hours, let's see how that works:

Juan is traveling 21 kmp. In three hours that's:
21(T) which is
21(3) = 63 Kilometers.

The brother is traveling 63 kmp. In T - 2 hours that's:
T - 2 which is 3 -2 = 1
63(1) = 63 Kilometers.

SOoo in 1 hour, the brother will be at the 63 kilometer mark. Since the brother took off at noon, in 1 hour it will be 1 pm. It will also be 1 pm for Juan if he travels for 3 hours from 10 a.m.

I hope this helps you. And a "sir" did not answer your question. :-) A girl did. :-) Sometimes math types are girls, too.
Good luck with your math.

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3 times a certain number plus 7 = 30

Just break it down to what they give you:

3 times: This is like saying:
a certain number: This is a number we don't know so we'll call it "x"
plus 7: This is
= 30

Put it all together: 3x + 7 = 30

Now solve for x like this:


(subtract 7 from both sides to isolate the "X")
()
(divide both sides by 3 to isolate the "x" further)

Plug in our "x" info and see if the statement is correct:

original equation
Plug into the "x" variable of this equation.

Yayyyy it works. :-)

I hope this helps you. :-)

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Original problem....


What you want to do is add together all the like terms. terms will add with other terms. Similarly, terms will add with other terms and so on......


It may help you if you re-write the problem with like terms underneath one another, like this:





When you do that you can see which terms go together, like this:



_______________________________


Where did we get that answer?? Break it down like this;







Now if you had a minus sign in front of a problem, like this:

you would have to distribute the minus sign. I mean to say that your problem would THEN become........

<----See how the became ? Also, see how the became ?

THEN you have.... which is




__________________


I hope this helps you. It's just a matter of adding like terms to one another. :-)

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(4+5i)(2-3i)


Use FOIL (first outside inside last)


First:
Outside:
Inside:
Last:

Let's put it all together:
Combine like terms:


We're not done yet. See the ?
Well, =

Therefore, for you really have: which is: 15

THEREFORE... you really have 8 - 2i + 15, which is.....
23 - 2i


See how that worked out? I hope this helps you. :-)

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A BOAT TRAVELING AT A SPEED OF 36 KM PER HOUR. IT HAS TO TRAVEL A DISTANCE OF 210 KM. HOW LONG WILL IT TAKE

You just need to know ONE equation about rate, time and distance.
You should always remember this equation:



Let's put it in terms of variables:
Let's call Rate: R
Let's call Time: T
Let's call Distance: D


So now we have:
or RT = D

What if you wanted to solve for R? Can you see that if you had RT = D that you could solve for "R" just by dividing T from both sides of the equation:

RT = D


What if you wanted to solve for T? Can you see that if you had RT = D, that you could solve for "T" just be dividing R from both sides of the equation:

RT = D


So now from just ONE equation: RT = D, you can "switch it around" so to speak and solve for Rate or you can solve for T.

In this problem, you want to solve for TIME. So, thinking of our one equation of RT = D, we realize we want to solve for T. Therefore, we should use this equation:


What do we know?
We know the Rate is 36 km per hour. R = 36
We know the Distance is 210 miles. D = 210


Let's plug that info in:





SO the boat must travel for 5 hours and .83 of an hour. OR....
5 hours and
.83 of 60 minutes which is: 49.8 minutes ()


The boat must travel for 5 hours and 49.8 minutes.

I hope this helps you. :-)

You can put this solution on YOUR website!
tickets for a basketball tournament were $6 for students and $9 for nonstudents. Total sales were $10,500, 250 more students tickets were sold than nonstudents. How many of each type of ticket were sold?

This is a "solve the system" type of problem where you need TWO equations.


Let's call the student tickets: S
Let's call the NON student tickets: N

You are told that S tickets are $6 and N tickets are $9.

Therefore, this equation works:
6S + 9N = $10,500
It makes sense, don't you think that the cost of the ticket is multiplied by the number of students who attend?

We need a 2nd equation tho and that comes from this info: 250 more students tickets were sold than nonstudents.

To put it another way: S = 250 + N
Do you see how this equation can represent that student tickets represented 250 MORE tickets than the non students?

Now put the two equations together and solve:
6S + 9N = $10,500
S = 250 + N <----you know what "S" equals, so let's plug that into the first equation.

6S + 9N = $10,500 First equation
6(250 + N) + 9N = 10,500 (See how we plugged (250 + N) into the "S" variable?)
1500 + 6N + 9N = 10,500 (Distributed the 6 to the 1500 and 6 to the N)
1500 + 15N = 10,500 (Combined like terms: 6N + 9N = 15N)
15N = 9000 (Subtracted 1500 from both sides to isolate the N)
N = 600 (Divided both sides by 15 to completely isolate the N)

Now we know that 600 non student tickets were sold.


Add 250 to the NON student tickets and we have 850 student tickets. OR.. just plug it into the 2nd equation:
S = N + 250
S = 600 + 250
S = 850

Does this check out?

Let's see:

Student tickets are $6
NON student tickets are $9
Total tickets sold: $10,500

6S + 9N = 10,500
6(850) + 9(600) = 10,500
5100 + 5400 = 10,500
10,500 = 10,500

YAY it works. I hope this helps you.