Write a two-step equation to represent each problem. 1. Jonelle spends \( \$ 22.50 \) at a library book sale. She spends \( \$ 4.50 \) on paperback books and buys 6 hardcover books of equal value. Determine the cost of each hardcover book. (Example 1) 2. Fatima orders model car kits, which cost \( \$ 7.50 \) each, from a hobby store. The store charges \( \$ 6.00 \) to deliver the kits, and Fatima spends a total of \( \$ 73.50 \). Determine the number of model car kits Fatima buys. (Example 1) 4. Mrs. Hernandez spends 41.25 minutes delivering mail in a neighborhood. It takes her 10 minutes to deliver mail to her first five houses. After that, it takes Mrs. Hernandez 1.25 minutes to deliver mail to each of the remaining houses. Determine how many houses still need their deliveries from Mrs. Hernandez. (Example 1) 6. Valerie replaces one car alternator every 1.75 hours. She takes a 1-hour lunch break. Determine how many alternators she replaces in 8 hours. (Example 1) 10
Upstudy AI Solution
Answer
Solution
Answered by UpStudy AI and reviewed by a Professional Tutor
Explain 
Simplify this solution The Deep Dive
1. Let \( x \) be the cost of each hardcover book. The equation representing Jonelle's spending is: \[ 4.50 + 6x = 22.50 \] To find \( x \), subtract 4.50 from both sides giving: \[ 6x = 18 \] Then, divide by 6: \[ x = 3 \] 2. Let \( y \) be the number of model car kits Fatima buys. The equation for her total spending is: \[ 7.50y + 6.00 = 73.50 \] Subtract 6.00 from both sides: \[ 7.50y = 67.50 \] Now, divide by 7.50: \[ y = 9 \] 3. Let \( h \) be the number of houses Mrs. Hernandez delivers to after the first five. The equation is: \[ 10 + 1.25h = 41.25 \] Subtract 10 from both sides: \[ 1.25h = 31.25 \] Dividing by 1.25 gives: \[ h = 25 \] 4. Let \( z \) be the number of alternators Valerie replaces. The total time equation she spends is: \[ 1.75z + 1 = 8 \] Subtracting 1 from both sides results in: \[ 1.75z = 7 \] Dividing by 1.75 gives: \[ z = 4 \]
