Question

The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number? Justify your reasoning.

Answer 1

I believe the answer would be 10/40. First, I simplified all of the given rations. You do this by finding the two numbers greatest common factor. For example, 3/12, 3 goes into 3 once and 3 goes into 12 four times. So that ratio would be 1/4. If you continue the pattern you would get 1/4 for all of them. Therefore, 10/40 would be correct since it's ratio would also be 1/4.

Answer 2

The value of the second number in the ratio is 40.

Given that the ratios in the table are equivalent :

We can express the ratio as a proportion :

3 : 12

x α y

3 α 12

3 = 12k

Where, k = constant of proportionality

We can solve for k

Divide both sides by 12 in other to isolate k

3/12 = 12k/12 = 1/4 = k

Hence, k = 1/4

General form of the relationship in the table can be expressed as ; x = 1/4y = x = y/4

If first Number in the ratio is 10;

Then the ratio looks like :

10 : y

x = 10 ; to find y

x = y/4

10 = y/ 4

Multiply both sides 4

10 × 4 = (y/4) × 4

40 = y

Hence, the second number is 40

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