8th Grade Linear Inequalities and Equations Challenge

1. Sarah has twice as many apples as Tom. If Tom has x apples, write an inequality to show that Sarah has more than 10 apples. Solve for x.

• x > 5

• x > 15

• x = 10

• x < 5

2. A store sells pencils for $0.50 each and erasers for $0.75 each. If you buy x pencils and y erasers, write an equation for the total cost if it is less than $10. Solve for y in terms of x.

• y < (20 - x) / 5

• y < (40 - 2x) / 3

• y < (50 - 3x) / 4

• y < (30 - x) / 2

3. A car rental company charges a flat fee of $30 plus $0.20 per mile driven. If you want to spend no more than $50, write an inequality and solve for the number of miles you can drive.

• 120 miles

• 100 miles

• 50 miles

• 75 miles

4. In a class, the number of boys is 5 more than twice the number of girls. If there are g girls, write an equation and solve for the number of boys in terms of g.

• b = 2g - 5

• b = 2g + 5

• b = g + 5

• b = 3g - 5

5. A concert hall has a seating capacity of 500. If x seats are reserved for VIPs and y seats are reserved for general admission, write an inequality to represent the situation and solve for y in terms of x.

• y < 500 - x

• y = 500 + x

• y ≥ 500 - x

• y ≤ 500 - x

6. A recipe requires 2 cups of flour for every 3 cups of sugar. If you have x cups of flour, write an equation to find how many cups of sugar you can use, and solve for sugar in terms of flour.

• s = (3/2)x

• s = (2/3)x

• s = 2x

• s = (4/3)x

7. A bike rental shop charges a $15 fee plus $2 per hour. If you want to spend less than $35, write an inequality and solve for the number of hours you can rent the bike.

• h < 15

• h < 5

• h < 8

• h < 10

8. The perimeter of a rectangle is 50 meters. If the length is x meters and the width is 5 meters, write an equation for the perimeter and solve for x.

• 15

• 25

• 20

• 30

9. A school is planning a field trip and has a budget of $200. If each student pays x dollars and there are y students, write an inequality to represent the budget and solve for y in terms of x.

• y = 200/x

• y >= 200/x

• y <= 200/x

• y < 200/x

10. A gardener has 3 times as many flowers as shrubs. If the total number of flowers and shrubs is less than 48, write an inequality and solve for the number of shrubs.

• s < 12

• s < 10

• s > 15

• s = 12