Question

Solve each problem by applying the four steps of problem solving. Use the strategy of solving an algebraic equation for each problem. In your part-time job selling kitchen knives, you have two different sets available. The better set sells for \(\$ 35\); the cheaper set, for \(\$ 20\). Last week you sold more of the cheaper set, in fact twice as many as the better set. Your receipts for the week totaled \(\$ 525 .\) How many of the better sets did you sell?

Short answer

Answer: 7 better sets were sold.

Step-by-step solution

Define variables

Let \(x\) represent the number of better sets sold and \(y\) represent the number of cheaper sets sold.

Translate the problem into equations

We are given that the better set sells for \(\$ 35\) and the cheaper set sells for \(\$ 20\). The total sales amount is \(\$ 525.\) From the information, we can establish the following equations: 1. The amount from selling the better sets and cheaper sets adds up to the total sales: \(35x + 20y = 525\) 2. Twice the number of better sets sold equals the number of cheaper sets sold: \(y = 2x\)

Solve the system of equations

Now we have to solve the system of equations to find the number of better sets (\(x\)) sold. We can use the substitution method by substituting the second equation into the first equation: \(35x + 20(2x) = 525\) Simplify the equation: \(35x + 40x = 525\) \(75x = 525\) Now, divide both sides by \(75\) to isolate \(x\): \(x = \frac{525}{75}\) \(x = 7\)

Find the number of better sets sold

Now that we have found \(x = 7\), we know the number of better sets sold is \(7\).