Challenge Your friend sells you a bicycle for ​$63 and a helmet for ​$21. The total cost is 150​% of what your friend spent originally. How much did your friend spend​ originally? How much money did your friend earn by selling the bicycle and helmet to​ you?

Question

Your friend originally spent ​$__
 
​(Round to the nearest dollar as​ needed.)

Answer 1

To find out how much your friend originally spent, we first need to determine the total amount you paid for the bicycle and helmet.

1. Calculate the total amount you paid:

   • Bicycle: $63
   • Helmet: $21
   • Total cost = Bicycle + Helmet = \(63 + 21 = 84\) dollars.

2. The total cost is 150% of what your friend originally spent: \[ 1.5 \times \text{Original Cost} = 84 \]

3. To find the original cost, divide the total cost by 1.5: \[ \text{Original Cost} = \frac{84}{1.5} = 56 \]

So, your friend originally spent $56.

4. Next, calculate how much money your friend earned by selling the bicycle and helmet:
   • Earnings = Total Paid - Original Cost
   • Earnings = \(84 - 56 = 28\) dollars.

In conclusion:

• Your friend originally spent $56.
• Your friend earned $28 by selling the bicycle and helmet to you.