Mastering Variables: Solve and Isolate in Word Problems

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an equation to represent the total number of apples Sarah has. If together they have 30 apples, how many apples does each person have?

• Tom has 10 apples, Sarah has 20 apples.

• Tom has 5 apples, Sarah has 25 apples.

• Tom has 15 apples, Sarah has 15 apples.

• Tom has 12 apples, Sarah has 18 apples.

3. A gardener has x flower pots. If he buys 5 more pots and gives away 3, he will have 2 pots left. Write an equation to find x and solve it.

• 10

• 0

• 3

• 5

4. A book costs $15 and a magazine costs $5. If you buy x books and y magazines for a total of $75, write an equation. If you bought 3 books, how many magazines did you buy?

• 6

• 7

• 5

• 4

5. In a class, the number of boys is x and the number of girls is 3x - 4. If there are 20 students in total, write an equation to find x and determine how many boys and girls are in the class.

• 4 boys and 16 girls

• 10 boys and 10 girls

• 8 boys and 12 girls

• There are 6 boys and 14 girls in the class.

6. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If you pay a total of $70 for renting a car, write an equation to find the number of miles driven.

• 200 miles

• 150 miles

• 100 miles

• 50 miles

7. A baker makes x loaves of bread. If he sells 3 loaves and then bakes 5 more, he will have 12 loaves. Write an equation to find x and solve it.

• 15

• 10

• 11

• 8

8. A school has x students in the morning session and 2x - 10 students in the afternoon session. If there are 50 students in total, write an equation to find x and determine the number of students in each session.

• Morning session: 25 students, Afternoon session: 25 students

• Morning session: 15 students, Afternoon session: 35 students

• Morning session: 10 students, Afternoon session: 40 students

• Morning session: 20 students, Afternoon session: 30 students

9. A store sells shirts for $20 each and pants for $30 each. If you buy x shirts and y pants for a total of $200, write an equation. If you bought 4 shirts, how many pairs of pants did you buy?

• 2

• 3

• 6

• 4

10. A cyclist travels x miles in the first hour and 2x miles in the second hour. If the total distance traveled is 90 miles, write an equation to find x and determine the distance traveled in each hour.

• First hour: 30 miles, Second hour: 60 miles

• First hour: 20 miles, Second hour: 70 miles

• First hour: 40 miles, Second hour: 50 miles

• First hour: 10 miles, Second hour: 80 miles