Question

how much does each one weigh? mashupmath 27.5 lbs 37.5 lbs mc 2.png 1 class comment logan kegley · 7:49 pm each pumpkin weighs 7.5 and each watermelon weighs 2.5

Explanation:

Step1: Define variables

Let $p$ = pumpkin weight (lbs), $w$ = watermelon weight (lbs)

Step2: Set up equations

First scale: $3p + 2w = 27.5$
Second scale: $4p + 3w = 37.5$

Step3: Eliminate one variable

Multiply first eq by 3: $9p + 6w = 82.5$
Multiply second eq by 2: $8p + 6w = 75$
Subtract the two: $(9p+6w)-(8p+6w)=82.5-75$
Simplify: $p = 7.5$

Step4: Solve for watermelon weight

Substitute $p=7.5$ into $3p+2w=27.5$:
$3(7.5) + 2w = 27.5$
$22.5 + 2w = 27.5$
$2w = 27.5 - 22.5 = 5$
$w = \frac{5}{2} = 2.5$

Answer:

Each pumpkin weighs 7.5 lbs, each watermelon weighs 2.5 lbs