help

a vendor sells a tool chest at $65.
She makes a 30% profit on each of the tool chests.
How much does she pay the manufacturer for each tool set?

\(\begin{array}{|rcll|} \hline $ 65 &=& $65 \cdot 100\ \% \\ $ 65 &=& $65 \cdot (30\ \% + 70\ \%) \\ $ 65 &=& \underbrace{$65 \cdot 30\ \%}_{\text{profit}} + \underbrace{ $65 \cdot 70\ \% }_{\text{manufacturer}} \\ \hline \end{array}\)

\(\begin{array}{rcll} \text{manufacturer} &=& $65 \cdot 70\ \%\\ &=& $65 \cdot 0.7 \\ &=& $45.5 \\ \end{array}\)

\(\begin{array}{rcll} \text{profit} &=& $65 \cdot 30\ \%\\ &=& $65 \cdot 0.3 \\ &=& $19.5 \\ \end{array}\)

\(\begin{array}{|rcll|} \hline $ 65 &=& \underbrace{$19.5}_{\text{profit}} + \underbrace{ $45.5 }_{\text{manufacturer}} \\ \hline \end{array}\)

Hmm!  If she pays the manufacturer $T and sells for $1.3T (30% increase on T) then:

1.3T = 65

T = 65/1.3 → 50

T = $50

i.e. she pays the manufacturer $50 for each tool chest.

She sells each chest for $65, having made 30% profit. Therefore, the price she paid to manufacturer before selling it at $65, is: $65/1.30 =$50 - which is the purchase price.