Question

The ratio of Brannon’s sport drinks to Telvin’s sport drinks was 3:1. When Brannon gave 10 sport drinks to Telvin, they each had the same amount. How many sport drinks did they have altogether?

Answer 1

B = Brannon’s sport drinks

T = Telvin’s sport drinks

The ratio of Brannon’s sport drinks to Telvin’s sport drinks was 3:1 means:

B / T = 3 / 1

B / T = 3

Multiply both sides by T

B = 3 T

When Brannon gave 10 sport drinks to Telvin, Branon will have B - 10 sport drinks.

Telvin will have T + 10 sport drinks.

When Brannon gave 10 sport drinks to Telvin, they each had the same amount means:

B - 10 = T + 10

Replace B by 3 T in this equation.

3 T - 10 = T + 10

Add 10 to both sides

3 T = T + 20

Subtract T to both sides.

2 T = 20

T = 20 / 2 = 10

Telvin has 10 sport drinks.

B = 3 T

B = 3 ∙ 10 = 30

Brannon has 30 sport drinks.

They altogether have 30 + 10 = 40 sport drinks

Check result.

The ratio of Brannon’s sport drinks to Telvin’s sport drinks was 3:1

B / T = 30 / 10 = 10 ∙ 3 / 10 ∙ 1 = 3 / 1 = 3:1

When Brannon gave 10 sport drinks to Telvin, they each had the same amount.

B - 10 = T + 10

30 - 10 = 10 + 10

20 = 20