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Math  /  Numbers & Operations

QuestionLack Dougnt a iarge box or microwave popcorn. The box contained 3 bags of butter-flavored popcorn for every 2 bags of plain popcorn.
Pick the diagram that models the ratio in the story.
If the box contained 12 bags of plain popcorn, how many bags of

Studdy Solution

STEP 1

1. The ratio of butter-flavored popcorn bags to plain popcorn bags is 3:2 3:2 .
2. The box contains 12 12 bags of plain popcorn.
3. We need to determine how many bags of butter-flavored popcorn are in the box.

STEP 2

1. Understand the ratio.
2. Set up a proportion.
3. Solve the proportion.

STEP 3

Understand the given ratio of butter-flavored popcorn to plain popcorn:
The ratio 3:2 3:2 means for every 3 3 bags of butter-flavored popcorn, there are 2 2 bags of plain popcorn.

STEP 4

Set up a proportion based on the given information:
Let x x be the number of bags of butter-flavored popcorn. The proportion based on the ratio is:
3 butter-flavored bags2 plain bags=x butter-flavored bags12 plain bags\frac{3 \text{ butter-flavored bags}}{2 \text{ plain bags}} = \frac{x \text{ butter-flavored bags}}{12 \text{ plain bags}}

STEP 5

Write the proportion:
32=x12 \frac{3}{2} = \frac{x}{12}

STEP 6

Solve the proportion by multiplying both sides by 12 12 to find x x .
32=x12 \frac{3}{2} = \frac{x}{12} (12)(32)=(x12)(12) (12)\left(\frac{3}{2}\right) = \left(\frac{x}{12}\right)(12) (12)(32)=x (12)\left(\frac{3}{2}\right) = x

STEP 7

Calculate the number of butter-flavored popcorn bags:
(12)(32)=362=18 (12)\left(\frac{3}{2}\right) = \frac{36}{2} = 18
The box contains:
18 bags of butter-flavored popcorn\boxed{18 \text{ bags of butter-flavored popcorn}}

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