In the summertime, Rick likes to buy cherries at the farmers market. On his first visit of the season, he bought 2 1/4 pounds of cherries. On his next visit, he bought 3 1/2 pounds of cherries and used a coupon to get $7 off his purchase. He noticed that he was charged the same amount each time. Which equation can you use to find p, the price of a pound of cherries? Choices: (A)2.25p = 3.5 + 7p (B)2.25p = 3.5p - 7 What is the price of a pound of cherries? ____ $

Question

In the summertime, Rick likes to buy cherries at the farmers market. On his first visit of the season, he bought 2 1/4 pounds of cherries. On his next visit, he bought 3 1/2 pounds of cherries and used a coupon to get $7 off his purchase. He noticed that he was charged the same amount each time. Which equation can you use to find p, the price of a pound of cherries?   Choices: (A)2.25p = 3.5 + 7p (B)2.25p = 3.5p - 7  What is the price of a pound of cherries?   ____ $

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. Rick bought 2 1/4 pounds of cherries on his first visit and 3 1/2 pounds on his second visit. He used a $7 coupon on the second visit. He was charged the same total amount on both visits. We need to find the price per pound of cherries, denoted as p.Convert to improper fractions: Convert mixed numbers to improper fractions to make calculations easier. 2 1/4 pounds = (2 * 4 + 1)/4 = 9/4 pounds 3 1/2 pounds = (3 * 2 + 1)/2 = 7/2 poundsSet up the equation: Set up the equation based on the information given. Since Rick was charged the same amount each time, the cost for the first visit (9/4 pounds at p dollars per pound) should equal the cost for the second visit (7/2 pounds at p dollars per pound minus the $7 coupon). (9/4)p = (7/2)p - 7Identify correct equation: Identify the correct equation from the choices given. The correct equation that represents the situation is (B) 2.25p = 3.5p - 7, which is the same as the equation we derived in Step 3 after converting the mixed numbers to decimals.Solve for p: Solve the equation for p. 2.25p = 3.5p - 7 Subtract 2.25p from both sides to get: 0 = 1.25p - 7 Add 7 to both sides to get: 7 = 1.25p Divide both sides by 1.25 to get: p = 7 / 1.25 p = 5.6

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