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?

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

1 answer

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.

  1. 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.
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