8th Grade Equations: Check & Interpret Your Solutions

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an equation to represent the situation and solve for x if Sarah has 18 apples. Check your solution by substituting back into the equation.

• 12

• 6

• 15

• 9

2. A movie theater charges $10 for adult tickets and $7 for child tickets. If the total revenue from selling x adult tickets and y child tickets is $200, write an equation and solve for y in terms of x. Interpret what this means in the context of ticket sales.

• y = (200 + 10x) / 7

• y = (200 - 10x) / 7

• y = (200 - 7x) / 10

• y = 200 - 10x

3. A store sells pencils for $0.50 each and erasers for $1.00 each. If the total cost for buying x pencils and y erasers is $10, write an equation and solve for y in terms of x. Check if your solution makes sense in the context of the problem.

• y = 5 - 0.25x

• y = 10 - 0.50x

• y = 10 - x

• y = 20 - 0.50x

5. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer pays $70, write an equation to find out how many miles they drove. Check your solution by substituting back into the equation.

• 80 miles

• 50 miles

• 120 miles

• 100 miles

6. A gardener has x square feet of garden space. If he plants tomatoes in 3x square feet and peppers in 2x square feet, and the total area is 50 square feet, write an equation and solve for x. Interpret the solution in the context of garden space.

• 20 square feet

• 10 square feet

• 15 square feet

• 5 square feet

7. A school is planning a field trip and has a budget of $500. If each student pays $25 and there are x students, write an inequality to represent the situation and solve for x. Check if your solution is valid in the context of the budget.

• x > 20

• x >= 25

• x < 20

• x <= 20

8. A recipe requires 2 cups of flour and 3 cups of sugar. If you want to make x batches of the recipe, write an equation for the total amount of flour and sugar needed. Solve for x if you have 12 cups of flour. Verify your solution by checking the amounts needed.

• 10 batches

• 4 batches

• 8 batches

• 6 batches

9. A bike rental shop charges a $15 fee plus $5 per hour. If a customer pays $35, write an equation to find out how many hours they rented the bike. Check your solution by substituting back into the equation.

• 2

• 4

• 6

• 8

10. A bookstore sells novels for $12 each and magazines for $5 each. If a customer buys x novels and y magazines for a total of $60, write an equation and solve for y in terms of x. Interpret what this means in the context of the purchase.

• y = 20 - 5x

• y = 12 - 2.4x

• y = 15 - 1.5x

• y = 10 - 3x