Question

braden wants to buy two pairs of the new shocktide sneakers in different colors. at vics sneaks, he can get 25% off one pair if he buys the other pair at full price. alternatively, he can use a coupon for $20 off if he buys two pairs at full price. after considering his options, braden realizes he would pay the same total amount for either option. which equation can you use to find p, the full price of one pair of shocktide sneakers? p + 0.75p = 2p - 20 2p - 0.25p = p + 20 what is the full price of one pair of shocktide sneakers?

Explanation:

Step1: Calculate the total cost for the first option

One pair is at full - price \(p\), and the other pair is at \(25\%\) off. The price of the discounted pair is \((1 - 0.25)p=0.75p\). So the total cost for the first option is \(p + 0.75p\).

Step2: Calculate the total cost for the second option

The full - price of two pairs is \(2p\). Using a \(\$20\) - off coupon, the total cost for the second option is \(2p-20\).

Step3: Set up the equation

Since the two total costs are equal, we have the equation \(p + 0.75p=2p - 20\).

Step4: Solve the equation for \(p\)

Combine like terms on the left - hand side: \(1.75p=2p - 20\).
Subtract \(1.75p\) from both sides: \(0 = 2p-1.75p - 20\).
Simplify: \(0 = 0.25p-20\).
Add \(20\) to both sides: \(20 = 0.25p\).
Divide both sides by \(0.25\): \(p=\frac{20}{0.25}=80\).

Answer:

The equation is \(p + 0.75p=2p - 20\), and the full - price of one pair of ShockTide sneakers is \(\$80\).