To make 5 gallons of cleaning solution, 3 cups of bleach is mixed in with water. Which table shows the relationship between the gallons of cleaning solution made and the cups of bleach used?

Option B.

Step-by-step explanation:

Let 'g' represent the number of gallons of cleaning solutions.

Let 'c' represent the number of cups of bleach.

From the question given above, we were told that:

To make 5 gallons of cleaning solution, 3 cups of bleach is mixed in with water.

This implies that number of gallons (g) of the cleaning solution is directly proportional to the number of cups (c) of the bleach mixed with water i.e

g ∝ c

g = Kc

K is the constant of proportionality.

Next, we shall determine the relationship between g and c as follow

g = 5

c = 3

K =?

g = Kc

5 = K × 3

Divide both side by 3

K = 5/3

g = Kc

K = 5/3

g = 5/3 c

Thus, the relationship between g and c is:

g = 5c / 3

Next, we shall make c the subject of the formula. This is illustrated below:

g = 5c / 3

Cross multiply

3g = 5c

Divide both side by c

c = 3g/5

Next, we shall determine c when g = 10, 15, and 20.

This is illustrated below:

g = 10

c =?

c = 3g/5

c = (3 × 10)/5 = 30/5 = 6

g = 15

c =?

c = 3g/5

c = (3 × 15)/5 = 45/5 = 9

g = 20

c =?

c = 3g/5

c = (3 × 20)/5 = 60/5 = 12

Summary:

Num. of gallon (g) >> Num. of cup (c)

5 >>>>>>>>>>>>>>>> 3

10 >>>>>>>>>>>>>>> 6

15 >>>>>>>>>>>>>>> 9

20 >>>>>>>>>>>>>>> 12

Therefore, option B gives the correct table.

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