Question

find the missing quantities by first computing the markup on one base and then computing the markup on the other. round rates to the nearest percent and dollar amounts to the nearest cent.

cost	markup	selling price	% markup on cost	% markup on selling price

cost	markup	selling price	% markup on cost	% markup on selling price

(round to the nearest cent or nearest percent.)

Explanation:

Step1: Recall the formula for % Markup on Selling Price

The formula for \(\%\) Markup on Selling Price is \(\%\text{ Markup on Selling Price}=\frac{\text{Markup}}{\text{Selling Price}}\times100\%\). Also, we know that \(\text{Selling Price}=\text{Cost}+\text{Markup}\). Let the Markup be \(M\) and Selling Price be \(S\). We know \(\text{Cost} = 15.30\), so \(S=15.30 + M\). And \(\%\text{ Markup on Selling Price}=45\%=\frac{M}{S}\times100\%\). Substitute \(S = 15.30+M\) into the markup formula: \(0.45=\frac{M}{15.30 + M}\).

Step2: Solve for Markup \(M\)

Cross - multiply: \(0.45\times(15.30 + M)=M\)
\(6.885+0.45M = M\)
Subtract \(0.45M\) from both sides: \(6.885=M - 0.45M\)
\(6.885 = 0.55M\)
Then \(M=\frac{6.885}{0.55}\approx12.52\) (rounded to the nearest cent)

Step3: Calculate Selling Price \(S\)

Since \(S=\text{Cost}+\text{Markup}\), \(S = 15.30+12.52 = 27.82\)

Step4: Calculate \(\%\) Markup on Cost

The formula for \(\%\) Markup on Cost is \(\frac{\text{Markup}}{\text{Cost}}\times100\%\). Substitute the values: \(\frac{12.52}{15.30}\times100\%\approx82\%\) (rounded to the nearest percent)

Answer:

Markup: \(\$12.52\), Selling Price: \(\$27.82\), \(\%\) Markup on Cost: \(82\%\)