A concrete mix calls for 1 part water, 3 parts cement, and 2 parts sand. Which of the mixtures below are in a proportional relationship with this blend?

A) 2 gal water, 6 gal cement, 4 gal sand
B) 3 gal water, 6 gal cement, 9 gal sand
C) 4 gal water, 12 gal cement, 8 gal sand
D) 5 gal water, 10 gal cement, 10 gal sand
E) 25 gal water, 8 gal cement, 5 gal sand

a. B and D
b. C and E
c. A and B
d. A and C

To determine the mixtures that are in a proportional relationship with the given blend, we need to compare the ratios of water, cement, and sand in each option to the ratio 1:3:2.

Explanation:

A proportional relationship exists when two quantities have a constant ratio. In this case, the concrete mix calls for 1 part water, 3 parts cement, and 2 parts sand. To determine which mixtures are in a proportional relationship, we need to check if the ratio between the quantities of water, cement, and sand are the same as the ratio 1:3:2. Let's analyze each option:

Option A: No, the ratio of water to cement to sand is not 1:3:2.
Option B: No, the ratio of water to cement to sand is not 1:3:2.
Option C: Yes, the ratio of water to cement to sand is 1:3:2.
Option D: No, the ratio of water to cement to sand is not 1:3:2.
Option E: No, the ratio of water to cement to sand is not 1:3:2.

Therefore, the mixtures that are in a proportional relationship with the given blend are options C and E.

Learn more about Proportional relationships here:

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