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A batsman in his 17th inning makes 85 scores and thereby increases his average by 3.
His average after 17th inning is?
:
let a = his average after the 17th inning
then
(a-3) = his average before the 17th
:
a =
multiply both sides by 17
17a = 16(a-3) + 85
17a = 16a - 48 + 85
17a - 16a = 37
a = 37 his average after 17 innings

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: A can do a work in 8 days and B in 12 days.
How long will A and B take to do the same work together?
:
Let t = time required when working together
Let the completed job = 1
:
+ = 1
multiply by 24 to clear the denominator, results:
3t + 2t = 24
t =
t = 4.8 days working together

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if 20 men can do a piece of work in 8 days,
20 * 8 = 160 man-days to complete the job
:
then how many men can finish the same work in 10 days?
let m = no. of men required to do the job in 10 days
10m = 160
m =
m = 16 men

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The combined area of a square and a rectangle is 116 square centimeters.
The width of the rectangle is 2 centimeters more than the length of a side of the square, and the length of the rectangle is 2 centimeters more than its width.
Find the dimensions of the square and the rectangle?
:
x = the side of the square and the width of the rectangle
:
Adding the two areas
x^2 + x(x+2) = 116
x^2 + x^2 + 2x = 116
A quadratic equation
2x^2 + 2x - 116 = 0
Solve this using the quadratic formula: a=2; b=2; c=-116

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A tire of a moving bicycle has radius 16 in.
If the tire is making 2 rotations per second, find the bicycle's speed in miles per hour.
:
2 * circumference * 3600 sec divided by inches in a foot and feet in a mile
:
Put this in your calc:
= 11.434 mph

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c(x+2)- 5 = b(x-3), solve for x
:
cx + 2c - 5 = bx - 3b
:
perform the necessary operations to get the x's on the left
cx - bx = -3b - 2c + 5
;
Factor out x
x(c-b) = -3b - 2c + 5
:
Divide both sides by (c-b)
x =

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= 5
multiply both sides by|1-8x|, results:
1 = 5|1 - 8x|
Rewrite it to
5|1 - 8x| = 1
divide both sides by 5
|1 - 8x| =
or
|1 - 8x| = .2
Remove the abs
1st solution
1 - 8x = .2
-8x = .2 - 1
-8x = -.8
Multiply both sides by -1
8x = .8
x =
x = .1
:
2nd solution
1 - 8x = -.2
-8x = -.2 - 1
-8x = -1.2
multiply both sides by -1
8x = 1.2
x =
x = .15
:
x = .1, .15
:
Did this do to your brain, what fiber is supposed to do the digestive tract?

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This is not an equation, no equal sign, so you can solve it, only simplify it.

The reciprocal gets rid of the -1 exponent and changes the ^-2 to ^2
=

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Find b and c so that y= -20x^2 +bx +c has vertex (-5,-3). Thanks, i already know that b= -200 but wasn't sure how to get c
:
So you have -20x^2 - 200x + c = y
Replace x and y
-20(-5^2) - 200(-5) + c = -3
-500 + 1000 + c = -3
500 + c = -3
c = -3 - 500
c = -503

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A bus traveled on a level road for 3 hours at an average speed 20 miles per hour faster than it traveled on a winding road.
The time spent on the winding road was 2 hours.
Find the average speed on the level road if the entire trip was 285 miles.
:
Let s = av speed on the level road
then
(s-20) = av speed on the winding road
:
Write a dist equation: dist = speed * time
:
Lev Rd dist + winding Rd dist = 285 miles
3s + 2(s-20) = 285
3s + 2s - 40 = 285
5s = 285 + 40
5s = 325
s = 325/5
s = 65 mph on level roads
:
:
Check solution
3(65) + 2(65-20) =
195 + 90 = 285

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let s = price of the senior cit ticket
let c = price of a child's ticket
:
Write an equation for each statement:
:
On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38.
3s + 1c = 38
;
The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.
3s + 2c = 52
:
Write the two equation for elimination
3s + 2c = 52
3s + 1c = 38
----------------subtraction eliminates s, find c
0 + 1c = $14 for one child ticket
:
Find s using the equation 3s + 1c = 38, replace c with 14
3s + 14 = 38
3s = 38 - 14
3s = 24
s = 24/3
s = $8 for each senior
:
:
You can check these solutions using the 2n equation




F

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Assume the problem is:
- 19 = -17
Add 19 to both sides
- 19 + 19 = -17 + 19
= +2
multiply both sides by 2 to get rid of the denominator, this leaves us with
f = 4
:
:
Check this in the original problem replacing f with
- 19 = -17
2 - 19 = -17
-17 = -17; confirms our solution

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Robert goes for a walk at a speed of 3 miles per hour.
Two hours later Roger attempts to overtake him by jogging at the rate of 7 miles per hour.
How long will it take him to reach Robert?
:
Let t = jogging time of Roger when overtakes Robert
then
(t+2) = walking time of Robert when he is overtaken
:
When this happens, they will both have traveled the same distance.
Write distance equation: dist = speed * time
;
Rog dist = Rob dist
7t = 3(t+2)
7t = 3t + 6
7t - 3t = 6
4t = 6
t = 6/4
t = 1.5 hrs of for Rog to overtake Rob
:
:
Check by finding the distances, they should be equal
7*1.5 = 10.5 mi
3(3.5) = 10.5 mi

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What is (x+5)^3 + 8 = 0
Subtract 8 from both sides
(x+5)^3 = -8
Find the cube root of both sides
x + 5 = -2
x = -2 - 5
x = -7
:
:
Check solution in original problem
(-7+5)^3 + 8 = 0
(-2)^3 + 8 = 0
-8 + 8 = 0; confirms our solution of x=-7

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A supplement of an angle is six more than three times the angle's complement. Write an equation to represent the problem and solve for the angle, its complement, and its supplement.
:
Let x = the angle
then
(180-x) = it's supplement
and
(90-x) = it's complement
:
The equation for the given statement:
(180-x) = 3(90-x) + 6
180 - x = 270 - 3x + 6
-x + 3x = 276 - 180
2x = 96
x = 96/2
x = 48 degrees is the angle
then
180 - 48 = 132 degrees is the supplement
and
90 - 48 = 42 degrees is the complement
;
:
Check our solutions in the given statement:
"A supplement of an angle is six more than three times the angle's complement."
132 = 3(42) + 6
132 = 126 + 6; confirms our solutions

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The perimeter of a triangle is 93 centimeters.
If two sides are equally long and the third side is 9 centimeters longer than the others, find the lengths of the three sides.
:
Let x = the length of the equal sides
then
(x+9) = the length of the 3rd side
:
2x + (x+9) = 93
3x = 93 - 9
3x = 84
x =
x = 28 is the length of the equal sides
and
28+9 = 37 is the length of the 3rd side

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A bus traveled 50 miles per hour and reached its destination in 6 hours.
How much longer would the trip have taken if the bus traveled 45 miles per hour?
:
Find the distance of the trip: 50 * 6 = 300 miles
:
Find the time at 45 mph: 300/45 = 6 hrs
:
It would have hr or 40 min longer

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Factor inside the radical to reveal perfect squares

extract the square root of these square

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A man came upon a bridge, he knew a train was coming soon, but he thought he could make it before the train came.
As he was 1/3 across the bridge he heard the train coming at 45 miles per hour. The man figured he had choice, he could run directly to the end of the bridge and get there at the exact same time as the train, but he also knew he could run back toward the train and get to the near end of the bridge just as the train got there.
How fast does the man run?
:
From the information given we can say that if he runs away from the train, he
will be 2/3 across bridge when the train enters the bridge
The train travels the full length of the bridge in the same time the man runs the remaining 1/3 length of the bridge.
therefore:
* 45 = 15 mph is how fast the man runs

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Jack is married to Jill. Their son, Junior, asked each of them to reveal their ages. Junior’s parents decided to tell him, but in the form of a puzzle. Jack told Junior,
:
Let x = the 10s digit of Jacks age
Let y - the units digit
:
“If you reverse the digits in my age, you get your mother’s age.
J = 10x + y
M = 10y + x
:
Jill told her son, “The sum of my age and your dad’s age is equal to 11 times the difference in our ages.”
(10x+y) + (10y+x) = 11[(10x+y) - (10y+x)]
10x + x + y + 10y = 11(10x - x - 10y + y
11x + 11y = 11(9x - 9y)
simplify, divide both sides by 11
x + y = 9x - 9y
y + 9y = 9x - x
10y = 8x
simplify, divide both sides by 2
5y = 4x
y = x
the only integer solution: x=5, y=4
:
Jack is 54, Mom is 45
;
:
See if that works out in the statement:
"The sum of my age and your dad’s age is equal to 11 times the difference in our ages.”
54 + 45 = 11(54-45)
99 = 11(9)

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pete stopped, but tim kept running for 11 laps more.
by the end of the run-a-thon, pete and tim had run 45 laps around the school playground altogether.
how many laps had each boy run?
:
let L = no. of laps run by Pete
then
(L+11) = no. of laps run by Tim
:
L + (L+11) = 45
2L = 45 - 11
2L = 34
L = 17 laps run by Pete and 28 laps run by Tim
:
:
Check 17 + 28 = 45

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A highway took 48 men 30 weeks to construct.
75 days into the construction phase, 8 men resigned,
Assuming that all men worked 7 days a week find the total number of days the project was delayed
:
Find the number of man-days to complete the highway (change weeks to days)
48 * (30*7) = 10,080 man-days
:
75 days into the construction phase, 8 men resigned,
48 * 75 = 3600
10080 - 3600 = 6480 more man-days required to complete the job
Let m = no. of days required by the 40 remaining men to complete the job
40m = 6480
m =
m = 162 days more days after the resignation of 8 men
:
Assuming that all men worked 7 days a week find the total number of days the project was delayed
30*7 = 210 days planned with 48 men
but
75 + 162 = 237 days actually required
;
237 - 210 = 27 day delay in completing the job

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Both car A and car B leave school at the same time, traveling in the same direction.
Car A travels at a constant speed of 77 km/h, while car B travels at a constant speed of 87 km/h.
How far is Car A from school 3.2 h later? Answer in units of km.
:
Write a distance equation; dist = speed * time
;
Car A dist = 3.2(77) = 246.4 km from the school
:
I don't see what Car B has to do with this problem!

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The monthly value of a share of ACME Corporation, in dollars, since January 2009 are shown in the table below. The values of the table below model the behavior of a quadratic function when it is graphed.
Month.......... Share Value (in dollars)
0...... 55
3...... 16
5...... 0
7...... -8
9..... -8
11.... 0
13.... 16
15..... 40

1. Using the table above, find the quadratic equation that represents the monthly value of a share of ACME Corporation since January 2009. Use the variable x to represent the number of months after January 2009 and the variable y to represent the monthly value.
:
Note that when x = 5 and x = 11, y = 0, therefore these are the x intercepts
(as the hint says); derive two factors and use FOIL to create a quadratic equation
(x-5)*(x-11) = x^2 - 11x - 5x + 55
y = x^2 - 16x + 55; is the equation
:
:
2. Find the y-intercept. Interpret the meaning of the y-intercept in relation to the given real-life scenario.
:
The y intercept occurs when x = 0, then y = 55
This would be the initial value in Jan 2009
:
:
3. Find the x-intercepts. Interpret the meaning of the x-intercepts in relation to the given real-life scenario.
From this we have to assume the share value was par (0) in March and June
:
:
4. From the equation you found in problem 1, what is the concavity of the parabola? How do you know? What is the lowest or maximum monthly value of a share of ACME Corporation and when did that occur?
:
we know from the fact that the coefficient of x^2 is positive, it is concave and has a minimum
Here is a graph of that equation, you can see for yourself

you can see that the min value is in Aug, (x=8), when the value is -9
which is the vertex, 8,-9
:
:
5. Using the quadratic equation you found in problem 1, predict the value of a share of ACME Corporation in October 2010?
Oct 2010, x = 22
:
y = x^2 - 16x + 55
y = 22^2 - 16(22) + 55
y = 484 - 352 + 55
y = 187 in Oct 2010
:
redraw our graph to show this

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You have a wire that is 53 cm long. You wish to cut it into two pieces.
One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle.
Let A represent the total area of the square and the circle.
What is the circumference of the circle when A is a minimum?
:
Let x = circumference of the circle
then
(53-x) = the perimeter of the square
and
= the side of the square
and
= the area of the square
:
Find the area of the circle using the circumference
find the radius (r)
2*pi*r = x
r =
r =
Find the area of the circle
A =
Replace r with
A = * = *
cancel pi into 39.48
A =
Total area of circle and square
A = + = +
:
convert these fractions to decimal coefficients
A(x) = .0796x^2 + .0625x^2 - 6.625x + 175.5625
A(x) = .1421x^2 - 6.625x + 175.5625
:
Find the axis of symmetry of this quadratic equation (min area)
x =
x =
x = 23.31 cm is the circumference when they have min area

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Todd contracted to paint a house for $480. It took him 4 hours longer than he anticipated, so he earned $0.50 less per hour than he originally calculated.
How long had he anticipated it would take him to paint the house?
:
Let t = no. of hr he anticipated to paint the house
then
(t+4) = no. of hrs he actually required to paint the house
:
= the hourly pay he anticipated
:
- = .50
multiply by t(t+4), results
480(t+4) - 480t = .5t(t+4)
480t + 1920 - 480t = .5t^2 + 2t
1920 = .5t^2 + 2t
A quadratic equation
.5t^2 + 2t - 1920 = 0
Multiply by 2 to give t^2 a coefficient of 1
t^2 + 4t - 3840 = 0
You can use the quadratic formula to find t, however this will factor to:
(t+64)(t-60) = 0
the positive solution
t = 60 hrs he anticipated to paint the House
:
:
Confirm this by finding the actual hourly pair
480/64 = $7.50, actual pay
480/60 = $8.00, hoped for pay

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The cold-water faucet fills a bathtub in 12min, and the hot-water faucet fills the bathtub in 10min.
If you remove the stopper, a full tub will empty in 6min. How long will it take to fill the tub if both faucets are on and the stopper is removed?
:
Let t = time to fill the tub with both faucets and drain open
Let a full tub = 1
:
+ - = 1
multiply by 60, to clear the denominators
60* + 60* - 60* = 1
cancel the denominators and you have:
5t + 6t - 10t = 60
11t - 10t = 60
t = 60 minutes

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A truck driving 260 miles over a flat interstate at a constant rate of 50 miles per hour gets 7 miles to the gallon. Fuel cost $3.50 per gallon.
For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon in its mileage.
Driver gets $27.50 per hour in wages and fixed cost for running the truck amount to $11.33 per hour.
What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip?
;
A. Let's start out by finding how long the trip will take?
= 5.2 hrs to make the 260 mi trip at 50 mph
:
B. Now, with this time known, how much will it cost to pay the driver and run the truck?
5.2 * 27.50 = $143.00, for the driver
5.2 * 11.33 = $58.92, for the truck
----------------------
total cost: $201.92
:
Cost for gas: * 3.50 = $130.00 for gas (at 50 mph)
add to the above cost: 201.92 + 130 = $331.92 total for the 260 mi trip
:
Correct a math error above, but also:
:
"What Constant Speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip? :
Speed affects time which affects cost
Speed also affect gas mileage
let s = speed
then
= time
and
= amt of gas required
:
Write a cost equation which is in terms of speed (s)
Cost = driver time + truck time + gas used
C(s) = *27.50 + *11.33 + *3.50

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let x = the 10's digit
let y = the units
then
10x+y = the number
:
"a two digit number is such that it is equal to 4 times the sum of it's digits."
10x + y = 4(x+y)
10x + y = 4x + 4y
10x - 4x = 4y - y
6x = 3y
simplify, divide by 2
2x = y
:
"when 27 is added to the number the total is equal to the same number when it's digits are interchanged."
10x + y + 27 = 10y + x
10x - x + 27 = 10y - y
9x + 27 = 9y
simplify, divide by 9
x + 3 = y
Replace y with 2x, (from the 1st statement)
x + 3 = 2x
3 = 2x - x
x = 3
y = 2(3)
y = 6
and
36 is the number
:
:
Check this in the 1st statement:
a two digit number is such that it is equal to 4 times the sum of it's digits.
36 = 4(3+6); confirms our solutions

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five times the difference of a number and two is the same as four times the
number.
find the number
:
write an equation for exactly for what it says:
5(n-2) = 4n
you should be able to solve this now

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John drove his car into the shop to fix the oil leak in his engine.
Once finished, his car was faster. He drove home in only 25 minutes when it took him 40 minutes to get there.
If he was traveling an average of 32 miles per hour going there, how fast did he drive home?
:
Change minutes to hours
= hrs
= hrs
:
Let s = his speed going home
:
The distance there and back are equal, write a dist equation; Dist = time * speed
:
s = (32)
mult both side by 12
5s = 8(32)
5s = 256
s =
s = 51.2 mph return speed
:
:
Confirm this by finding the distances, they should be equal
*51.2 = 21.33 mi
*32 = 21.33 mi