Grade 7 Math: Expressions & Linear Equations Challenge

1. Sarah has 3 times as many apples as Tom. If Tom has x apples, write an expression for the number of apples Sarah has and simplify it. What if Tom has 5 apples?

2. A rectangle has a length that is 4 more than its width. If the width is w, write an equation for the perimeter of the rectangle and solve for w when the perimeter is 36.

3. The sum of a number and 12 is equal to 30. Write an equation to represent this situation and solve for the number.

4. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an expression for the total cost of renting the car for m miles and evaluate it for 100 miles.

5. If 5 times a number decreased by 7 equals 18, what is the number? Write the equation and solve it step by step.

6. The cost of a concert ticket is $25 plus a service fee of $5. Write an expression for the total cost of buying t tickets and simplify it. What is the total cost for 3 tickets?

7. A store is having a sale where you can buy 2 shirts for the price of 1. If each shirt costs p dollars, write an expression for the total cost of buying s shirts and simplify it. What if s is 4?

8. The equation 2x + 3 = 15 represents the number of hours x a student studies. Solve for x and interpret what this means in a real-world context.

9. A gardener is planting flowers in rows. If each row has 6 flowers and there are r rows, write an expression for the total number of flowers and evaluate it for 4 rows.

10. A linear equation representing the relationship between hours worked (h) and pay (p) is p = 15h. Graph this equation for h values from 0 to 8 and interpret the slope.