Question

1. a bike shop sells you a bicycle for $63 and a helmet for $21. the total cost is 150% of what the shop spent originally. a. how much did the shop spend originally? b. how much profit did the bike shop earn by selling the bicycle and helmet to you?

Explanation:

Part a

Step1: Calculate total selling price

The selling price of the bicycle is $63 and the helmet is $21. So total selling price $S = 63 + 21 = 84$ dollars.

Step2: Let original cost be $x$

We know that the total cost (selling price) is 150% of the original cost. So $150\%$ of $x$ is $S$. Mathematically, $1.5x = 84$ (since 150% = 1.5).

Step3: Solve for $x$

To find $x$, we divide both sides of the equation by 1.5: $x=\frac{84}{1.5}=56$ dollars.

Step1: Recall total selling price and original cost

Total selling price $S = 84$ dollars (from part a) and original cost $x = 56$ dollars (from part a).

Step2: Calculate profit

Profit $P$ is selling price minus original cost. So $P = S - x = 84 - 56 = 28$ dollars.

Answer:

The shop spent originally $\$56$.

Part b