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Set up and solve a proportion to answer the question.

The ratio of lime to sand in mortar is 3:7. How much lime must be mixed with 28 bags of sand to make mortar?

Answer :

To solve this problem, we need to set up a proportion based on the given ratio of lime to sand in the mortar, which is 3:7. This means that for every 3 parts of lime, there are 7 parts of sand.

Here's how we can find out how much lime is needed for 28 bags of sand:

1. Understand the ratio: The ratio is given as 3:7, which means for every 3 units (or parts) of lime, there are 7 units (or parts) of sand.

2. Set up the proportion: We want to find out how many bags of lime [tex]\( x \)[/tex] are needed for 28 bags of sand. Using the ratio 3:7, you can set up the proportion as follows:
[tex]\[
\frac{3}{7} = \frac{x}{28}
\][/tex]

3. Solve the proportion: To find [tex]\( x \)[/tex], you can cross-multiply and solve for [tex]\( x \)[/tex]:
[tex]\[
3 \times 28 = 7 \times x
\][/tex]
[tex]\[
84 = 7x
\][/tex]

4. Calculate [tex]\( x \)[/tex]: Divide both sides by 7 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{84}{7} = 12
\][/tex]

Thus, you need to mix 12 bags of lime with 28 bags of sand to maintain the 3:7 ratio in the mortar.

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