Question

1. Fifteen more than half a number is 9.

2. Eight more than four times a number is -12.
3. Amy has saved $725 for a new guitar and lessons. Her guitar costs $475, and guitar lessons are $25 per hour. Determine how many hours of lessons she can afford.

Answer 1

1. x = -12

2. x = -5

3. 10 hours

Explanation:

You can write each as an equation and solve it by converting the words to math symbols:

• more than is +
• half a number is 0.5x
• a number is x
• four times a number is 4x
• is =

1. "Fifteen more" is 15 + and "half a number" is 0.5x "is 9" = 9.

Together it becomes 15 + 0.5x = 9. Solve using inverse operations:

15 + 0.5x = 9

15-15+0.5x = 9-15

0.5x = -6

x= - 12

2. "Eight more" is 8 + "than four times a number" is 4x and equals -12.

Together it becomes 8 + 4x = -12. Solve using inverse operations:

8 + 4x = -12

8-8 +4x = -12 - 8

4x = -20

x = -5

3. If Amy has saved $725 then this is the most she can spend. She spends $475 for the guitar. This means that $725 - $475 = $250. She can spend $250 for the lessons. To find how many lessons divide the money left by the lesson price. 250/25 = 10. She can take 10 hours of lessons.