Braden wants to buy two pairs of the new ShockTide sneakers in different colors. At Vic's 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? Choices: (A)2p - 0.25p = p + 20 (B)p + 0.75p = 2p - 20 What is the full price of one pair of ShockTide sneakers? ____ $

Question

Braden wants to buy two pairs of the new ShockTide sneakers in different colors. At Vic's 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?   Choices: (A)2p - 0.25p = p + 20 (B)p + 0.75p = 2p - 20  What is the full price of one pair of ShockTide sneakers?   ____ $

Bytelearn · Accepted Answer

Analyze Options for Braden: Let's analyze the options given to Braden for buying two pairs of sneakers. If he gets 25% off one pair, the discount is 0.25p for that pair, and he pays the full price for the other pair, which is p. So, the total cost with the discount on one pair is p (full price for the first pair) + 0.75p (75% of the full price for the second pair after the discount).Calculate Total Cost with Discount: On the other hand, if he uses the $20 off coupon, he pays the full price for both pairs, which is 2p, and then subtracts the $20 discount. So, the total cost with the coupon is 2p - 20.Calculate Total Cost with Coupon: Since Braden realizes he would pay the same total amount for either option, we can set the two total costs equal to each other to find the full price of one pair of sneakers. The equation that represents this situation is p + 0.75p = 2p - 20.Set Equations Equal: Now, let's solve the equation p + 0.75p = 2p - 20. First, combine like terms on the left side of the equation: p + 0.75p = 1.75p.Combine Like Terms: Next, rewrite the equation with the combined terms: 1.75p = 2p - 20.Isolate Variable p: To isolate p, we need to get all the terms with p on one side. Subtract 1.75p from both sides of the equation: 1.75p - 1.75p = 2p - 1.75p - 20.Add to Isolate Term: This simplifies to 0 = 0.25p - 20. Now, add 20 to both sides to isolate the term with p: 20 = 0.25p.Divide to Solve for p: Finally, divide both sides by 0.25 to solve for p: 20 / 0.25 = p.Perform Division: Perform the division to find the value of p: 80 = p.

Full solution

More problems from Solve linear equations with variables on both sides: word problems

Related topics