A store marks up the wholesale cost of a small appliance by to set a regular selling price. During a promotional sale, the appliance is advertised at off the regular selling price, and a sales tax of is applied to the discounted price at checkout. If a customer pays a final total of \$59.40, what was the wholesale cost of the appliance, in dollars?

Solution available with step-by-step explanation

SAT Percentages Question 30 | Free SAT Prep | Aniko

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Question 30·Hard·Percentages

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A store marks up the wholesale cost of a small appliance by $50\%$ to set a regular selling price. During a promotional sale, the appliance is advertised at $20\%$ off the regular selling price, and a sales tax of $10\%$ is applied to the discounted price at checkout. If a customer pays a final total of $59.40, what was the wholesale cost of the appliance, in dollars?

Your answer

(Express the answer as an integer)

For chained percentage problems (markup, discount, tax, etc.), convert each step into a multiplier of the form $1 \pm \text{decimal}$ , apply them in order, and either combine them into one overall multiplier or work backward by dividing to undo each step. Avoid adding or subtracting the percentages directly; instead, set up an equation like $(\text{original}) \times (\text{multiplier}_1) \times (\text{multiplier}_2) \dots = (\text{final})$ and solve for the original value. This keeps the work organized and minimizes arithmetic mistakes under time pressure.

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Represent the unknown price

Let $x$ represent the wholesale cost. How can you write the regular selling price if the store adds a $50\%$ markup to $x$ ?

Turn each percentage into a multiplier

Remember: increasing by $p\%$ means multiplying by $1 + \frac{p}{100}$ , and decreasing by $p\%$ means multiplying by $1 - \frac{p}{100}$ . What multipliers correspond to $50\%$ markup, $20\%$ off, and $10\%$ tax?

Combine the multipliers and use the final price

Starting from $x$ , multiply by the three multipliers in order to get an expression for the final checkout price in terms of $x$ . Set that equal to $59.40 and solve for $x$ .

Desmos Guide

Use a single expression to find the wholesale cost

In Desmos, type the expression 59.40/(1.5*0.8*1.1) or equivalently 59.40/1.32. The value that Desmos outputs is the wholesale cost of the appliance.

Step-by-step Explanation

Define the variable and model the markup

Let $x$ be the wholesale cost (in dollars).

A markup of $50\%$ means the regular selling price is the original plus half of it:

\text{regular price} = x + 0.5x = 1.5x

Model the 20% discount

A discount of $20\%$ means the customer pays $80\%$ of the regular price.

So the discounted price is:

\text{discounted price} = 1.5x \times 0.8 = 1.2x

Model the 10% sales tax and set up the equation

A sales tax of $10\%$ means the customer pays $110\%$ of the discounted price, so we multiply by $1.1$ :

\text{final price} = 1.2x \times 1.1 = 1.32x

We are told this final price is $59.40, so:

1.32x = 59.40

Solve for the wholesale cost

Solve the equation from the previous step by dividing both sides by $1.32$ :

x = \frac{59.40}{1.32}

Compute this division:

\frac{59.40}{1.32} = 45

So the wholesale cost of the appliance is $45$ .

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Desmos Guide

Step-by-step Explanation

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Step-by-step Explanation