Infinite Pre-Algebra: Two-Step Equation Word Problems Worksheet ... - Free Printable

I can see a worksheet with two-step equation word problems. Let me solve each problem carefully.

Problem 1:
Jill bought 5 shirts and 3 pairs of pants for $87. Each shirt cost $12. How much did each pair of pants cost?

Let p = cost of each pair of pants
5(12) + 3p = 87
60 + 3p = 87
3p = 87 - 60
3p = 27
p = 9

Each pair of pants cost $9.

Problem 2:
A high school band sold 45 concert tickets. Adult tickets were $8 and student tickets were $5. They made $300 total. How many adult tickets were sold?

Let a = number of adult tickets
Let s = number of student tickets

a + s = 45 (total tickets)
8a + 5s = 300 (total money)

From first equation: s = 45 - a
Substitute into second equation:
8a + 5(45 - a) = 300
8a + 225 - 5a = 300
3a + 225 = 300
3a = 75
a = 25

25 adult tickets were sold.

Problem 3:
The sum of three consecutive numbers is 72. What are the numbers?

Let n = first number
n + (n+1) + (n+2) = 72
3n + 3 = 72
3n = 69
n = 23

The numbers are 23, 24, and 25.

Problem 4:
The sum of three consecutive even numbers is 90. What are the numbers?

Let n = first even number
n + (n+2) + (n+4) = 90
3n + 6 = 90
3n = 84
n = 28

The numbers are 28, 30, and 32.

Problem 5:
You bought a magazine for $3 and some candy bars for $2 each. You spent $11 total. How many candy bars did you buy?

Let c = number of candy bars
3 + 2c = 11
2c = 8
c = 4

You bought 4 candy bars.

Problem 6:
Maria bought some boxes of crackers at $3 each and some bottles of juice at $2 each. She bought twice as many boxes of crackers as bottles of juice. She spent $24 total. How many of each did she buy?

Let j = number of bottles of juice
Let c = number of boxes of crackers

c = 2j (twice as many crackers as juice)
3c + 2j = 24 (total cost)

Substitute c = 2j into second equation:
3(2j) + 2j = 24
6j + 2j = 24
8j = 24
j = 3

So c = 2(3) = 6

She bought 6 boxes of crackers and 3 bottles of juice.

Problem 7:
Samantha wrote 40 pages before lunch playing basketball in the afternoon. She gave her friend 10 pages to read. Then she wrote 15 more pages. How many pages does she have?

40 - 10 + 15 = 45

She has 45 pages.

Problem 8:
Jason spent half of his weekly allowance playing video games. He then spent $4 on snacks. After that he had $6 left. What is Jason's weekly allowance?

Let a = weekly allowance
a/2 - 4 = 6
a/2 = 10
a = 20

Jason's weekly allowance is $20.

Final Answer:
1. $9 per pair of pants
2. 25 adult tickets
3. 23, 24, 25
4. 28, 30, 32
5. 4 candy bars
6. 6 boxes of crackers and 3 bottles of juice
7. 45 pages
8. $20