Chris rented a truck for one day. There was a base fee of 14.99, and there was an additional charge of 78 cents for each mile driven. Chris had to pay 243.53 when he returned the truck. For how many miles did he drive the truck?

14.99 + 0.78x=243.53
0.78x-243.53-14.99
x=243.53-14.99/0.78
x=293

17.99+0.93x=280.25
x=280.25 - 17.99/0.93
x=




Jina received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.24 per pound. After buying the coffee, she had $62.28 left on her card. How many pounds of coffee did she buy?
90 - 7.24x = 68.28
-7.24x = 68.28-90
x=68.28-90/-7.24
x=3

70 - 7.72x = 23.68
x=23.68 - 70/-7.72

6

-2u -21 >_ -11

-2u -21 +21 >_ -11 + 21

-2u >_ 10

-2u/-2 <_ 10/-2

u <_ -5


5u < -25
5u/5 < -25/5

u < -5

-24>-6x
4<x

20>_-5x

-4<_x


A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $13,005, and the variable costs will be $20.50 per book. With the other method, the one-time fixed costs will total $37,469 , and the variable costs will be $9.50 per book. For how many books produced will the costs from the two methods be the same?


13,005+20.5x = 37,469+9.5x
20.5x-9.5x = 37,469 - 13,005
11x = 24,464
x= 24464/11
x=2224

16994+19.25x = 48584+11.75x
19.25x-11.75x = 48584 - 16994
7.5x = 31590
x=4212





Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $19
 monthly fee and charges an additional $0.12
 for each minute of calls. The second plan has no monthly fee but charges $0.17
 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
19 + 0.12x = 0.17x
19 = 0.17x - 0.12x
19 = 0.05x
19/0.05 = x
380 = x
15 + 0.11x = 0.15x
15 = 0.15x - 0.11x
15 = 0.04x

20 + 0.14x = 0.19x
20 = 0.19x - 0.14x
20 = 0.05x
20/0.05x
x=400

17 + 0.13x = 0.17x
17 = 0.17x - 0.13x
17 = 0.04x
17/0.04x
x=425



At the city museum, child admission is $5.30 and adult admission is $8.50. On Wednesday, 172 tickets were sold for a total sales of $1212.40. How many adult tickets were sold that day?

5.30(172)-5.30x + 8.50x = 1212.40
911.60 + 3.20x = 1212.40
3.20x=300.80
x=300.80/3.20
x=94

5.30(158)-5.30x + 9.10x = 1164.20
837.40 + 3.80x = 1164.20
3.80x=326.8
x=326.8/3.80
x=86 adult



Deandre's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Deandre $5.45
 per pound, and type B coffee costs $4.30
 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $815.40 How many pounds of type A coffee were used?

5.45x+4.30(4x) = 815.40
5.45x+17.20x=815.40
22.65x=815.40
x=815.40/22.65
x=36

4.35x+5.55(3x)=420.00
4.35x+16.65x=420.00
21x=420.00
x=420.00/21
x=20




A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the high-quality version is 4.6 MB. Yesterday, the high-quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 3364
 MB. How many downloads of the standard version were there?

2.4x+9.2x=3364
11.6x=3364
x=3364/11.6
x=290

2.5x+12.9x=4466
15.4x=4466
x=4466/15.4
x=


At the city museum, child admission is $6.00  and adult admission is $9.80. On Thursday, twice as many adult tickets as child tickets were sold, for a total sales of $896.00. How many child tickets were sold that day?
6.00x+9.80(2x)=896.00
6.00x+19.60x=896.00
25.60x=896.00
x=896/25.60
x=35

5.40x+9.50(4x)=998.20
5.40x+38x=998.20
43.4x=998.20
x=998.20/43.4
x=23





-4w - 25 >_ 2w + 17
-4w -2w - 25 >_ 2w - 2w + 17
-6w-25>_ 17
-6w >_ 42
w<_ -7
-3w<_12
w>_-4



To rent a certain meeting room, a college charges a reservation fee of $47  and an additional fee of $7.30 per hour. The history club wants to spend less than $112.70 on renting the meeting room.

Rental cost < 112.70
47+7.30t < 112.70
7.30t< 65.70
/7.30

t < 9

rental cost < 72.20
47 + 6.30t < 72.20
6.30t < 25.2
t < 4



rental cost < 78.60
33+5.70t < 78.60
5.70t < 45.60
t <_ 8





Mai is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $147  and allows unlimited mileage. Company B has an initial fee of $75  and charges an additional $0.90 for every mile driven.

$147 < $75 + 0.90m
72 < 0.90 m
/0.90
80<m or m>80

91 < 55 + 0.80m
36 < 0.80 m
45<m

127 < 55 + 0.90m
72 < 0.90m

93 < 75 + 0.90
18 < 0.90m


In the lab, Hans has two solutions that contain alcohol and is mixing them with each other. He uses 4
 times as much Solution A as Solution B. Solution A is 19%
alcohol and Solution B is 12%
 alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 616 millimeters of pure alcohol

0.19(4x) + 0.12x=616
0.76x +0.12x =616
0.88x = 616
x = 616/0.88
x = 700

0.16(4x) + 0.11x=150
0.64x + 0.11x = 150
0.75x = 150
x= 150/0.75
x = 200

0.16(3x) + 0.13x = 488
0.48x + 0.13x = 488
0.61x = 488
x= 488/0.61
x= 800



Two factory plants are making TV panels. Yesterday, Plant A produced 3 times as many panels as Plant B. Four percent of the panels from Plant A and 3% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 900 defective panels

0.04(3x) + 0.03x = 900
0.12x + 0.03x = 900
0.15x = 900
x = 900/0.15
x=6000

0.04(3x) + 0.03x = 1350
0.12x + 0.03x = 1350
0.15x = 1350
x = 1350/0.15
x=9000

0.04(4x) + 0.05x = 1470
0.16x + 0.05x = 1470
0.21x = 1470
x = 1470/0.21
x= 7000


Jenny invested her savings in two investment funds. The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B. Fund A returned a 6% profit and Fund B returned a 5% profit. How much did she invest in Fund B, if the total profit from the two funds together was $2070?

0.06(3x) + 0.05x = 2070
0.18x + 0.05x= 2070
0.23x = 2070
x = 2070/0.23
x=9000

0.04(3x) + 0.03x = 1800
0.12x + 0.03x = 1800
0.15x = 1800
x = 1800/0.15
x=12000