Equation Mastery: Translate & Validate Real-World Scenarios

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 14 apples. Check your solution for validity.

• 10

• 5

• 7

• 12

2. A store sells notebooks for $3 each and pens for $2 each. If the total cost for y notebooks and z pens is $30, write an equation and solve for y if z is 5. Verify your solution.

• 10

• 4

• 8

• 6

4. 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 the number of miles driven and solve it. Validate your answer.

• 120

• 80

• 90

• 100

5. Emily is three years older than her brother. If the sum of their ages is 25, write an equation to find their ages and solve for Emily's age. Check your solution for accuracy.

• 16

• 14

• 10

• 12

6. 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 and solve for x if you have 12 cups of flour. Verify your solution.

• 4

• 8

• 6

• 10

7. The perimeter of a rectangle is 50 meters. If the length is 5 meters more than the width, write an equation to find the dimensions of the rectangle and solve for the width. Check your solution by calculating the perimeter.

• 20 meters

• 15 meters

• 5 meters

• 10 meters

8. A school is planning a field trip and has a budget of $500. If each student pays $25, write an inequality to determine how many students can attend. Solve the inequality and check if your solution is valid.

• 25

• 15

• 30

• 20

9. A gardener has 30 feet of fencing to create a rectangular garden. If the length is twice the width, write an equation to find the dimensions of the garden and solve for the width. Validate your answer by checking the perimeter.

• 5 feet

• 15 feet

• 10 feet

• 7 feet

10. A book costs $15 and a magazine costs $5. If a customer buys x books and y magazines for a total of $100, write an equation to find the number of books purchased if 5 magazines were bought. Solve and check your solution.

• 7

• 3

• 10

• 5