Question

holy sells marky a bicycle for $114 and a helmet for $18. the total cost for marky is 120% of what holy spent originally to buy the bike and helmet.how much did hely spend originally? how much money did he make by selling the bike and helmet to marky.

Answer 1

The total cost for Marky (TCM) is the cost of the bike plus the cost of the helmet:

`\text{TCM}=114+18=132`

And since the total cost for Marky is 120% the original cost for Holy (OCH), we can express it like this:

`\begin{gathered} 120\text{\%}=(TCM)/(OCH)*100\text{\%} \\ 120\text{\%}=(132)/(OCH)*100\text{\%} \\ \end{gathered}`

Solving for OCH, we get:

`\begin{gathered} 120\text{\%}=(132)/(OCH)*100\text{\%} \\ \frac{120\text{\%}}{100\text{\%}}=(132)/(OCH)*\frac{100\text{\%}}{100\text{\%}} \\ 1.2=\frac{132}{\text{OCH}} \\ \text{OCH}*1.2=132\frac{OCH}{\text{OCH}} \\ \text{OCH}*1.2=132 \\ \text{OCH}=(132)/(1.2)=110 \end{gathered}`

Then the original cost for Holy (OCH) is $110, and the total amount of money that Marky made is $132