Question

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a mechanics tool set is on sale for 280 after a markdown of 30% off the regular price. find the regular price.
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solve.
a battery with a discount price of $55 is on sale for 26% off the regular price. find the regular price. round to the nearest cent.
$
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a car dealer advertises a 4% markup over cost. find the selling price of a car that costs the dealer $18,000.
$

Explanation:

Step1: Set up the equation for the first problem

Let the regular price be \(x\). After a \(30\%\) markdown, the sale price is \((1 - 0.30)x=0.7x\). We know \(0.7x = 280\).

Step2: Solve for \(x\) in the first problem

Divide both sides of the equation \(0.7x = 280\) by \(0.7\): \(x=\frac{280}{0.7}=400\).

Step3: Set up the equation for the second problem

Let the regular price of the battery be \(y\). After a \(26\%\) markdown, the sale price is \((1 - 0.26)y = 0.74y\). We know \(0.74y=55\).

Step4: Solve for \(y\) in the second problem

Divide both sides of the equation \(0.74y = 55\) by \(0.74\): \(y=\frac{55}{0.74}\approx74.32\).

Step5: Set up the equation for the third problem

Let the cost of the car be \(C = 18000\). The markup is \(4\%\), so the selling price \(S=(1 + 0.04)C\).

Step6: Solve for \(S\) in the third problem

Substitute \(C = 18000\) into the equation \(S=(1 + 0.04)\times18000\). First, \(1+0.04 = 1.04\), then \(S=1.04\times18000 = 18720\).

Answer:

\(400\)
\(74.32\)
\(18720\)