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Three consecutive integers, x, (x+1), (x+2)
:
The sum of three consecutive integers are arranged such that twice the middle integer is equal to 9 more than the largest.
2(x+1) = (x+ 2) + 9
:
2x + 2 = x + 11
:
2x - x = 11 - 2
;
x = 9 is the 1st integer
:
What is the sum of the three integers?
9 + 10 + 11 = 30
:
:
Check solution in the statement:
"twice the middle integer is equal to 9 more than the largest."
2 * 10 = 11 + 9

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what is the answer to this:
Let x = "a number"
:
"the square root of the sum of a number and 7 is 8."
= 8
:
x + 7 = 64; squared both sides
:
x = 64 - 7
:
x = 57
:
:
Check solution:
= 8

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Find the values of the positive numbers a and b,
:
given that a is 8 times the size of b
a = 8b
:
and the reciprocal of ab is 1 less than 3.
+ 1 = 3
: = 2; subtract 1 from both sides
2ab = 1
:
2(8b*b) = 1; substitute 8b for a
16b^2 = 1
b^2 =
b =
b = 1/4
then
a = 8*
a = 2
:
:
Check solution in the statement:"a is 8 times the size of b"
2 = 8 * (1/4)

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A line passing through (-4,4) and (x,-8) is perpendicular to a line with slope 5/12. Find the value of x.
:
m1 = slope of the given coordinates
m2 = 5/12
;
We know that the relationship of the slopes of perpendicular lines is:
m1 * m2 = -1
m1 * = -1
Multiply equation by 12:
m1 * 5 = -12
m1 =
:
Using the slope formula; (y2-y1)/(x2-x1) = m:
=
:
You can see that x has to = 1, but here is the algebra to solve it:
=
neg on both sides:
=
cross multiply, solve for x:
12(x+4) = 12 * 5
12x + 48 = 60
12x = 60 - 48
12x = 12
x = 1

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Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on earth also varies according to the elevation of the object? In particular the weight of an object follows this equation: w=cr^-2, where C is a constant, and r is the distance that the object is from the center of the earth. Use 1 mile = 5,280 feet.
:
Question: Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.
:
Using the given equation w = c*r^-2, substitute 100 for w and 3,963 for r, find c:
:
c * 3963^-2: = 100
:
Same as
c = 100
:
c = 100 * 3963^2
:
c = 1.57(10^9)

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1.A ball is thrown vertically upward with an initial velocity of 160 feet per second. The distance in feet of the ball from the ground after 1 second is s =160t - 160t^2. For what is the interval of time is the ball less than 336 feet above the ground (after it is tossed until it returns to the ground)
:
I think the equation for this type of problem would be s = 160t - 16t^2:
:
Find the interval above 336 ft
Arrange as a quadratic equation
-16t^2 + 160t < 336
-16t^2 + 160t - 336 > 0
Simplify and change the signs, divide equation by -16
+t^2 - 10t = 21 = 0
Factor
(t-7)(t-3) = 0
t = 7; t = 3
Here is the graph of the equation y = -16t^2 + 160t
You can see the ball will be above 336 ft during the 4 sec interval between 3 sec and 7 sec.

You can also see that the ball will be less than 336 ft during the intervals
0 to 3 sec
7 to 10 sec
:
:
2.Use the compound interest formulas A=P(1 +r/n)^nt and A =P^ert to solve.
Suppose you have 9000 dollars to invest. Which investment yields the greater return over 5 years: 6.25% compounded continuously or 6.3% compounded semi annually?
:
Find the interest compounded semi-annually at 6.3% for 5 years
A = 9000 * (1 + .063/2)^(2*5)
A = 9000 * (1.0315)^10; use a calc
A = 9000 * 1.363617
A = 12,272.55
:
Find it a continuous interest after 5yrs at 6.25%:
Here I think the continuous interest formula should be P*e^rt
A = 9000 * e^(.0625*5); use a calc
A = 9000 * 1.366838
A = 12,301.54
:
:
3. Graph the polynomial function f(x) = -6x^4 + 9x^3:
If you factor this, it will give you a range of the values of x to plot
-3x^3(2x - 3)= 0
So you have x = 0 and x = +1.5, so plot this from -1 to + 2 at .5 intervals
x | y
-------
-1 | -15
-.5| -1.5
0 | 0
+.5|+.75
+1 |+3
1.5| 0
2 |-24
:
Your graph should look like this:

:
Hope this helps you out.

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The first store he enters sells his favorite size nails at 9 cents per pound. At this price, the carpenter realized that he would be short $7.15 if he tried to buy the nails. The carpenter goes to a competing hardware store and finds that the nails sell for 6 cents a pound. He realizes that after paying for the nails, he would have $2.45 left over. How many pounds of nails is he trying to buy?
:
Let x = lb of nails required
Let y = amt of money he has
:
Write an equation for each store:
.09x = y + 7.15
.06x = y - 2.45
We can also write it, subtract and eliminate y:
.09x - y = 7.15
.06x - y = -2.45
----------------
.03x = +9.60
x =
x = 320 lb of nails
:
check solution by finding the cost of each; the dif should be 7.15 + 2.45 = 9.60
320*.09 = 28.80
320*.06 = 19.20
----------------
differs by 9.60

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How do I find out how much the 'a' is worth in "5a-2 = 3a-7" ??
:
Perform some simple algebra operations to get "a" on the left by itself:
5a - 2 = 3a - 7
:
add 2 to both sides (gets rid of the -2 on the left):
5a = 3a - 7 + 2
:
5a = 3a - 5
:
Subtract 3a from both sides (gets rid of the 3a on the right)
5a - 3a = -5
:
2a = -5
:
divide both sides by 2, (gives you 1a or just a)
a =
a = -2.5
:
:
Prove to yourself that this is, in fact, true;
substitute -2.5 for a in the original equation:
5(-2.5) - 2 = 3(-2.5) - 7
-12.5 - 2 = -7.5 - 7
-14.5 = -14.5; equality reigns, so it is true

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A cyclist traveled at a rate of 24 mi/h to visit a nearby town . The cyclist averaged 18 mi/h on the return trip. If the round trip took 4.9 hours, find the one way distance to the nearby town.
:
Let d = distance to town
:
Write a time equation: Time = dist/speed
:
Time to + time back = 4.9 hrs
+ = 4.9
Multiply equation by 432 (18*24) to get rid of the denominators:
432* + 432* = 432*4.9
Cancel the denominators and you have:
18d + 24d = 2116.8
:
42d = 2116.8
d =
d = 50.4 miles
:
:
Check solution:
50.4/24 + 50.4/18 =
2.1 + 2.8 = 4.9

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An arrow is shot upward and outward from atop a 81-foot cliff, with an initial velocity of 132 feet per second. The height of the rocket t seconds after launch is given by the equation h= -16t^2 + 132t +81.
:
The max height will occur at the axis of symmetry
Find the axis of symmetry using the formula: x = -b/(2a);
:
In this equation it would be:
t =
t =
t = +4.125 sec the arrow will be at the greatest altitude
:
Find the greatest altitude reached by the arrow. Round to the nearest foot.
:
Substitute 4.125 for t in the given equation
h = -16(4.125^2) + 132(4.125) + 81
:
h = -16(17.015625) + 544.5 + 81
:
h = -272.25 + 625.5
:
h = 353.25 ~ 353 ft is max height

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The revenue R (in millions of dollars) of a large retail store can be modeled by R=1.23t^2-2.22t+8.5, where t is the number of years since 1990. Estimate the year in which the store's revenue will reach 90 million dollars?
:
Replace R with 90 and solve for t
1.23t^2 - 2.22t + 8.5 = 90
:
1.23t^2 - 2.22t + 8.5 - 90 = 0
:
1.23t^2 - 2.22t - 81.5 = 0
:
Use the quadratic formula:
In this equation: a=1.23, b=-2.22, c=-81.5

:

:

:

Positive solution

t =
t = 9.09 ~ 9 yrs; 1999 is the year of 90 million dollars

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Ethel tosses a softball upward. When the ball leaves her hand 5 feet above the ground it has an initial upward velocity of 66 feet per second. How high can Ethel toss the ball?
:
Using the equation h = -16t^2 + 66t + 5; find the axis of symmetry (x=-b/(2a):
t =
t =
t = 2.0625 sec, when the ball reaches max height
:
Substitute 2.0625 in the equation to find h:
h = -16(2.0625^2) + 66(2.0625) + 5;
:
h = -16(4.2539) + 136.125 + 5
:
h = -68.0625 + 141.125
:
h = 73 ft max height of the ball

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What are the pros and cons of solving quadratic equations using graphing, using the quadratic formula, completing the square, and factoring.
:
This my opinion on this:
:
If you have graphing calc, graphing is 1st, otherwise it's last
;
Next is factoring (if it will factor)
:
Next completing the square if the coefficient of x^2 = 1 and the math is easy
:
next is quadratic formula

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simplify

Multiply by conjugate of (5+i), namely (5-i)
* = =
:
= =
:
How about this; could you follow what we did here? Any questions?

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In the time it takes to fly 360 miles with a head wind, she can only fly 240 mies against the headwind. if the speed of the plane in still air is 150 mph, find the wind speed.
:
Let x = the wind speed
then
(150-x) = ground speed against the wind
and
(150+x) = ground speed with the wind
:
write a time equation: Time = dist/speed
:
With time = Against time
=
Cross multiply
240(150+x) = 360(150-x)
;
36000 + 240x = 54000 - 360x
:
240x + 360x = 54000 - 36000
:
600x = 18000
x =
x = 30 mph is the wind speed
:
:
Check solution in original equation: Against speed = 120, With speed = 180
= ; confirms our solution

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x = 10's digit
y = units
:
"find the two-digit number whose tens digits is 4 less than its units digits"
x = y - 4
:
"if the original number is 2 more then 3 times the sum of the digits"
10x + y = 2 + 3(x+y)
:
10x + y = 2 + 3x + 3y
:
10x - 3x = 3y - y + 2
:
7x = 2y + 2
Substitute (y-4) for x, find y
7(y-4) = 2y + 2
:
7y - 28 - 2y + 2
:
7y - 2y = 2 + 28
:
5y = 30
y =
y = 6
therefore:
x = 6 - 4 = 2
:
Our solutions is 26
;
Check solution using the statement:
""if the original number is 2 more then 3 times the sum of the digits"
26 = 2 + 3(2+6)
26 = 2 + 24

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A hot-water heater is in the shape of a circular cylinder. It has a height of 3 feet 9 inches and a diameter of 16 inches. How many gallons of water will the tank hold? (1 cubic foot-7.5 gallons. Round to the nearest tenth, if necessary.
:
The volume of a cylinder: V = pi*r^2*h
:
radius = 16/2 = 8"
:
Convert 3' 9" to inches: (12*3) + 9 = 45"
:
V = pi*8^2*45
V = pi*64*45
V = 9047.8 cubic inches
:
Convert to cubic ft
= 5.236 cu ft
:
5.236 * 7.5 = 39.3 gal.

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Dr. Bennington took an alloy containing 10% silver and mixed it with an alloy containing 40% silver to get a 60 ounce alloy containing 30% silver. How many ounces of the 10% alloy did he use?
:
Let x = amt of 10% alloy required
then
(60-x) = amt of 40% silver
:
.10x + .40(60 - x) = .30(60)
:
.1x + 24 - .4x = 18
:
.1x - .4x = 18 - 24
:
-.3x = -6
x =
x = +20 oz of 10% alloy required

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+ = 2
:
Multiply equation by the common denominator; (3x-4)(x-1)
(3x-4)(x-1)* + (3x-4)(x-1* = 2(3x-4)(x-1)
;
Cancel out the denominators, FOIL on the right
3(x-1) + 2(3x-4) = 2(3x^2 - 7x + 4)
:
Multiply what's inside the brackets:
3x - 3 + 6x - 8 = 6x^2 - 14x + 8
;
9x - 11 = 6x^2 - 14x + 8
:
Combine on the right:
0 = 6x^2 - 14x - 9x + 8 + 11
:
A quadratic equation:
6x^2 - 23x + 19 = 0
:
To find the 0's use the quadratic formula:
a=6; b=-23 c=19

:
You should get two solutions:
x = 2.62867 and x = 1.20467

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Find the length of the sides of a square if the number of square meters in its area is 1.5 times the number of meters in its perimeter.
:
Let x = side of the square
:
x^2 = 1.5(4x)
x^2 = 6x
x^2 - 6x = 0
x(x-6) = 0
x = 6 meters

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3.) Flying to Kampala wit ha tailwind a plane averaged 158 km/h. On the retun trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
:
Let x = speed of the plane in still air
Let y = speed of the wind
Write an equation for each trip:
x + y = 158
x - y = 112
------------adding eliminates y, find x
2x = 270
x =
x = 135 km/hr is the speed of he plane in still air
Find y using the equation: x + y = 158
135 + y = 158
y = 158 - 135
y = 23 km/ hr is the speed of the wind
:
:
4.) The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
:
Let x = no. of Sr tickets
let y = no. of child's tickets
write an equation for each day:
3x + 1y = 38
3x + 2y = 52
------------- subtracting eliminates x, find y
0x - 1y = -14
y = $14 is the cost of a child's tickets
Find x using the 1st equation:
3x + 14 = 38
3x = 38 - 14
x =
x = $8 cost of a Sr ticket
Check solution in 2nd equation: 3(8) + 2(14) = 52
:
;
6.)A boat traveled 210 miles downstream and back. The trip downstream took 10 hours. The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of the current?
:
Let x = speed of the boat
Let y = speed of the current
Write a distance equation for each trip dist = time * speed
10(x+y) = 210
70(x-y) = 210
Simplify both equations, divide the 1st one by 10 and the 2nd one by 70, results:
x + y = 21
x - y = 3
-------------adding eliminate y, find x
2x = 24
x =
x = 12 mph speed of the boat
then
12 + y = 21
y = 21 - 12
y = 9 mph speed of he current.
I'll let you check solutions in one of the original equations.
:
:
7) The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54
students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
:
Let x = no. of students in each van
Let y = no. of students in each bus
Write an equation for each school
8x + 8y = 240
4x + 1y = 54
Multiply the 2nd equation by 2 and subtract from the 1st equation
8x + 8y = 240
8x + 2y = 108
-----------------subtracting eliminates x, find y
you should be able to take it from here now
:
:
8) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
1x + 6y = 372
4x + 12y = 780
;
Multiply the 1st equation by 2, subtract the 2nd equation
2x + 12y = 744
4x + 12y = 780
---------------
you carry on from here
:
:
9) Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?
3x + 9y = 75
8x + 5y = 67
Multiply 1st equation by 8, and 2nd equation by 3
24x + 72y = 600
24x + 15y = 201
-------------------subtracting eliminates x, find y
Carry on from here
:
:
10) Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the
cost each of one small box of oranges and one large box of oranges.
3x + 14y = 203
11x +11y = 220
:
;
11) A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
12(x+y) = 336
14(x-y) = 336
:
:
12) DeShawn and Shayna are selling flower bulbs for a school fundraiser. Customers can buy bags of windflower bulbs and bags of daffodil bulbs. DeShawn sold 10 bags of windflower bulbs and 12 bags of daffodil bulbs for a total of $380. Shayna sold 6 bags of windflower bulbs and 8 bags of daffodil bulbs for a total of $244. What is the cost each of one bag of windflower bulbs and one bag of daffodil
bulbs?
10x + 12y = 380
6x + 8y = 244
I am totally out of time. Hope this helps. This many problems at once will usually not be considered by most tutors.

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Three workers are to accomplish a job.the first worker can finish a job in 4 hours.the second worker can finish a job in 2 hours working together find the amount of time it would take the third worker to do the job on him own.
;
There is something missing in this problem, check it carefully

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One number exceeds another by 5. The sum of their reciprocals equal to 19
divided by the product of the two numbers. Find the two numbers.
:
(a) How will you set up the problem?
(b) What is the equation that the one number exceeds another by 5?
(c) What is the product of two numbers, in terms of x?
(d) What is x? Also check your answer.
:
I'll do the problem and let you answer the questions from that:
Let x = "one number"
Let y = "another number
:
Write an equation for the statement,"One number exceeds another by 5."
x = y + 5
or
y = (x-5)
:
Write an equation for:
"The sum of their reciprocals equal to 19 divided by the product of the two numbers."
=
In terms of x; replace y with (x-5)
=
solve for x: multiply equation by x(x-5) to get rid of the denominators, results:
1(x-5) + 1x = 19
x -5 + x = 19
2x = 19 + 5
x =
x = 12
:
y = 12 - 5 = 7
:
Check solution in original equation
=
=

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The speed of a stream is 5km/h. If a boat travels 76kms downstream in 2 hrs less time than it takes to travel 54km upstream, what is the speed of the boat in still water.
:
Here is a better approach. If we write a time equation, we only have 1 unknown
Let r = speed of boat in still water
then
(r-5) = speed upstream
(r+5) = speed downstream
:
Time = dist/speed:
Time upstream - 2 hrs = time downstream
- 2 =
:
Get rid of the denominators, multiply equation by (r+5)(r-5):
(r+5)(r-5)* - 2(r+5)(r-5) = (r+5)(r-5)*
:
Cancel out the denominators:
54(r+5) - 2(r^2-25) = 76(r-5)
:
54r + 270 - 2r^2 + 50 = 76r - 380
:
-2r^2 + 54r - 76r + 270 + 50 + 380 = 0
:
-2r^2 - 22r + 700 = 0
Simplify divide equation by -2 and you have:
r^2 + 11r - 350 = 0
Factor this to:
(r-14)(r+25) = 0
The positive solution:
r = +14 is the speed in still water
:
:
Check solution by finding the time for each:
speed upstream = 9 mph; speed downstream = 19 mph
54/9 = 6 hrs
76/19 = 4
----------
diff = 2 hrs

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Alexandra constructed a rectangular pen for her dog using a side of the barn for one side and 26 meters of fencing for the remaining three sides. If the area enclosed was 72 square meters, find the dimensions of the pen.
:
Since it only has 3 sides of fencing, we can write the perimeter equation:
2L + W = 26
Therefore:
W = (26-2L); use this for substitution
:
The area
L * W = 72 sq/m
:
Substitute (26-2L) for W;
L(26-2L) = 72
:
26L - 2L^2 = 72
:
-2L^2 + 26L - 72 = 0; a quadratic equation
:
Simplify, divide equation by -2
L^2 - 13L + 36 = 0
Factor to:
(L-9)(L-4) = 0
Two solutions:
L = 9 or L = 4
:
L is usually the longer dimension, use L = 9
then
W = 26 - 2L
W = 26 - 2(9)
W = 8 m is the width
:
Check the solution find the perimeter and the area:
2(9) + 8 = 26
and
9*8 = 72

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1. The sum of the ages of John and Jacob is 20 years. Two years from now , one will be thrice as old as the other then. Find their present ages.
:
Jo + Ja = 20
Jo = (20 - Ja); use for substitution
:
Write an equation for the statement:
"Two years from now , one will be thrice as old as the other then."
Jo + 2 = 3(Ja + 2)
Jo + 2 = 3Ja + 6
Jo = 3Ja + 6 - 2
Jo = 3Ja + 4
Substitute (20-Ja) for Jo
20 - Ja = 3Ja + 4
20 - 4 = 3Ja + Ja
16 = 4Ja
Ja =
Ja = 4 yrs
:
Jo = 20 - 4 = 16 yrs old
:
:
2. The sum of the ages of Manny and Dennis is 47 years.
M + D = 47
M = 47 - D
;
Seven years ago, Manny was twice as old as Dennis was then.
M - 7 = 2(D-7)
:
How old is each now?
Solve this one the same way as we did the 1st one.

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a chemist needs 10 liters of a 25 % acid solution. the solution is to be mixed from three solutions whose acid concentrations are 10% 20% 50% how many liters of each solution should the chemist use to satisfy the following
:
a use as little as possible the 50% solution
Mix it with 20% solution only
Let x = amt of 50% solution
then
(10-x) = 20% solution
equation:
.50(x) + .20(10-x) = .25(10)
.5x + 2 - .2x = 2.5
.3x = 2.5-2
x =
x = 1.67 liters of 50% solution required
10 - 1.67 = 8.33 liters of 20% solution
:
;
b use as much as possible of the 50% solution
Mix it with the 10% solution only
Let x = amt of 50% solution
then
(10-x) = 10% solution
equation:
.50x + .10(10-x) = .25(10)
.5x + 1 - .1x = 2.5
.4x = 2.5 - 1
x =
x = 3.75 liters of 50% solution
10 - 3.75 = 6.25 liters of 10% solution
;
:
c use 2 liters of the 50% solution
Mix it with 10% and the 20%; they will have to equal 8 liters
Let x = 20% solution
then
(8-x) = 10% solution
equation:
.20x + .10(8-x) + .50(2) = .25(10)
.20x + .8 - .10x + 1 = 2.5
.2x - .1x + 1.8 = 2.5
.1x = 2.5 - 1.8
.1x = .7
x =
x = 7 liters of 20% solution
(8-7 = 1 liter of the 10% solution
:
:
Check the last one:
.2(7) + .1(1) + .5(2) = .25(10)
1.4 + .1 + 1 = 2.5

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Bernie is the oldest of the four Bryant brothers. Bobby is twice as old as Billy, but 2 years younger then Bernie. Bernie is twice as old as Buddy. The youngest Bryant brother is 6 years old. What are the ages of the four Bryant brothers?
:
From the given statements, here's what I think is the Oldest to youngest:
Let a = Bernie's age
Let b = Bobby's age
Let c = Buddy's age
Let d = Billy who is 6
:
Bobby is twice as old as Billy (who is 6)
b = 2(6) = 12 is Bobby's age
:
but 2 yrs younger than Bernie
a = 12 + 2 = 14 is Bernie's age
:
Bernie is twice as old as Buddy
a = 2c
Bernie is 14, therefore:
c = 7 is Buddy's age
;
My answer:
Bernie is 14
Bobby is 12
Buddy is 7
Billy is 6

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When the baton twirler releases the baton into the air with an initial velocity of 30ft per sec and 5ft from the ground. She will catch the baton when it falls back to a height of 6ft, How many seconds is the baton in the air?
:
h=-16t^2 + vt + s
:
h= final height (6 ft); I changed this to the "final height"
t= time in motion (solve for the time in seconds)
s= initial height 5 ft
v=initial velocity 30 ft/sec
:
-16t^2 + vt + s = h
:
Substitute the given values:
-16t^2 + 30t + 5 = 6
;
-16t^2 + 30t + 5 - 6 = 0
:
-16t^2 + 30t - 1 = 0
:
We need to use the quadratic formula here:

In this equation: a=-16; b=30; c=-1



The positive solution:


t = +1.84 sec is the time the baton is in the air
:
:
you can check the correctness of this solution, substitute 1.84 for t in:
h= -16t^2 + 30t + 5 to see if you get h~6

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Help with translating this into a quadratic equation to solve. Thanks!
A photo is 3 inches longer that it is wide. A 2 inch border is placed around the photo making the total area of the photo and border 108in^2. What are the dimensions of the photo?
:
Let x = width of the photo
then
(x+3 = the length of the photo
:
The dimensions of the total area (photo and border):
(x+4) = width
and
(x+3)+4 =
which is:
(x+7) = length
:
Total area equation:
(x+4)(x+7) = 108
FOIL
x^2 + 11x + 28 = 108
:
x^2 + 11x + 28 - 108 = 0
The quadratic equation
x^2 + 11x - 80 = 0
:
:
Solve this for x to get the width of the photo

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The equation d=rt represents the formula for total distance traveled. The distance traveled, d, is equal to the rate of travel, r, multiplied by the time of travel, t. Use this formula to help solve the following problem.
Tina and Tim work together and are planning to take a trip this weekend. On Friday afternoon, Tina gets a head start and leaves work in her car traveling at 45 mph. Three hours later, Tim leaves work on the same road at 65 mph. Assuming there is no traffic, in how many hours will Tim pass Tina?
:
A. Who will be driving longer and by how much?
B. Once Tim catches up with Tina, who will have gone the farther distance?
C. What equation represents this situation?
D. Solve the equation; show your work
E. How many hours did it take Tim to pass Tina?
:
I'll solve the problem and let you answer the above questions from that:
:
Let t = time for Tim to catch up with Tina
Then
(t+3) = Tina's travel time, when Tim catches up
:
When Tim catches Tina they will have gone the same distance (ans question B)
Write a distance equation from this fact; Dist = speed * time:
:
Tim's dist = Tina's dist
65t = 45(t+3)
65t = 45t + 135
65t - 45t = 135
20t = 135
t =
t = 6.75 hrs for Tim to catch up with Tina
:
:
Confirm our solution by finding the distance traveled by each (should be equal):
(Tina' travel time: 6.75 + 3 = 9.75)
9.75 * 45 = 438.75 mi
6.75 * 65 = 438.75 mi