Question

1. a store sells $2\frac{1}{4}$ pounds of mulch for every $1\frac{1}{2}$ pounds of gravel sold. the store sells 180 pounds of mulch and gravel combined. how many pounds of each item does the store sell?

□ pounds of mulch
□ pounds of gravel

Explanation:

Step1: Convert mixed numbers to fractions

$2\frac{1}{4} = \frac{9}{4}$, $1\frac{1}{2} = \frac{3}{2}$

Step2: Find ratio of mulch to gravel

$\text{Ratio} = \frac{9}{4} : \frac{3}{2} = \frac{9}{4} \div \frac{3}{2} = \frac{9}{4} \times \frac{2}{3} = \frac{3}{2} = 3:2$

Step3: Calculate total parts of ratio

$3 + 2 = 5$ parts

Step4: Find weight per part

$\frac{180}{5} = 36$ pounds per part

Step5: Calculate mulch weight

$3 \times 36 = 108$ pounds

Step6: Calculate gravel weight

$2 \times 36 = 72$ pounds

Answer:

108 pounds of mulch
72 pounds of gravel