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Word Problems
100

Solve for b:

a + b = 12

b = 12 - a


WORK

a + b = 12

-a          -a

      b = 12 - a

100

Solve for r:

|r-6|=10

r={16,-4}

100
Solve for m:

5 = 5m - 23 + 2m
m =4

WORK
5 = 5m - 23 + 2m
5 = 5m + 2m - 23
5 = 7m - 23
5 + 23 = 7m - 23 + 23
28 = 7m
28/7 = 7m/7
4 = m
100

Solve for b:


3b - 4 = b + 2

b = 3


WORK

3b - 4 = b + 2

3b - 4 + 4 = b + 2 + 4

3b = b + 6

3b - b = b - b + 6

2b = 6

2b/2 = 6/2

b = 3

100
Solve:

Five friends equally split a restaurant bill that comes to $32.50. How much does each friend pay?
Each friend pays $6.50.

WORK
5x = 32.50
5x/5 = 32.50/5
x = 6.5 ~~~> $6.50
200

Solve for P:

PV=nRT

P=(nRT)/V



200

Solve for m:

|6-m|=4

m={2,10}

200
Solve for x:

(x + 4) + 2x = 67
x = 21

WORK
(x + 4) + 2x = 67
x + 2x + 4 = 67 [addition is commutative]
3x + 4 = 67
3x + 4 - 4= 67 - 4
3x = 63
3x/3 = 63/3
x = 21
200
Solve for x:

5x + 2 = 2x + 14
x = 4

WORK
5x + 2 = 2x + 14
5x + 2 - 2 2x + 14- 2
5x = 2x + 12
5x - 2x = 2x - 2x + 12
3x = 12
3x/3 = 12/3
x = 4
200
Solve:

You work for 4 hours on Saturday and 8 hours on Sunday. You receive a $50 bonus. You earn $164.00 total. How much did you earn per hour?
You earned $9.50 per hour.

WORK
4x + 8x + 50 = 164
12x + 50 = 164
12x + 50 - 50 = 164 - 50
12x = 114
12x/12 = 114/12
x = 9.5 ~~~> $9.50
300

Solve for a:

A=(ab)/2

a=(2A)/b


300

Solve for n:

|6-10n|=44

n={-19/5,5}

300
Solve for x:

-8(2x - 1) = 36
x = -7/4

WORK
-8(2x - 1) = 36
-16x + 8 = 36 [Distributive Property]
-16x + 8 - 8 = 36 - 8
-16x = 28
-16x/(-16) = 28/(-16)
x = -7/4
300
Solve for p:

1.5p = 1.25p + 8
p = 32

WORK
1.5p = 1.25p + 8
1.5p - 1.25p = 1.25p - 1/25p + 8
0.25p/0.25 = 8/0.25
p = 32
300
Write an equation that represents "the value of y is 4 less than 9 times x"

y=9x-4

400

Solve for k:

k/x=v+w

k=xv+xw



400

Solve the equation: 

|-5r+5|+4=24

x={-3,5}

400
Solve for x:

3.5 - 0.02x = 1.24
x = 113

WORK
3.5 - 0.02x = 1.24
100*(3.5 - 0.02x) = 1.24*100
350 - 2x = 124 [Distributive Property]
350 - 350 - 2x = 124 - 350
-2x/(-2) = -226/(-2)
x = 113
400
Solve for x:

2(5x - 1) = 3(x + 11)
x = 5

WORK
2(5x - 1) = 3(x + 11)
10x - 2 = 3x + 33 [Distribute]
10x - 3x - 2 = 3x - 3x + 33
7x - 2 + 2 = 33 + 2
7x/7 = 35/7
x = 5
400
Solve

Online concert tickets cost $37 each, plus a service charge of $8.50 per ticket. The Web site also charges a transaction fee of $14.99 for the purchase. You paid $242.49. How many tickets did you buy?
You bought 5 tickets.

WORK
37t + 8.50t + 14.99 = 242.49
45.5t + 14.99 = 242.49
45.5t + 14.99 - 14.99 = 242.49 - 14.99
45.5t = 227.5
45.5t/45.5 = 227.5/45.5
t = 5 ~~~> 5 tickets
500

Solve for a:

k-a=w+v

a=k-w-v



500

Solve the equation: 

(|10x-4|)/7=4


x={16/5,-12/5}

500
Solve for x:

3x/4 - x/3 = 10

[remember what fractions really look like?]
x = 24

WORK
3x/4 - x/3 = 10
9x/12 - 4x/12 = 10 [write fractions/common denominator]
5x/12 = 10
12*(5x/12) = 10*12
5x/5 = 120/5
x = 24
500

What are the TWO possible first steps to solve this equation? 

1/2(2+4x)=x+5

Multiply both sides of the equation by 2, which would result in 2+4x=2x+10

OR

Distribute the 1/2 to remove the parentheses, resulting in 1+2x=x+5

500

Solve


Pristine Printing will print business cards for $0.10 each plus a setup charge of $15. The Printing Place offers business cards for $0.15 each with a setup charge of $10. What number of business cards costs the same from either printer?

Printing 100 cards would cost the same from either business.


WORK

0.10n + 15 = 0.15n + 10

0.10n - 0.10n + 15 = 0.15n - 0.10n +10

15 = 0.05n + 10

15 - 10 = 0.05n + 10 - 10

5 = 0.05n

5/0.05 = 0.05n/0.05

100 = n ~~~>100 cards