P6 Math: Money Donation

Tanya, Mariah, and Devi donated some money to charity. Tanya donated 2/3 as much as the total donation made by Mariah and Devi. Mariah donated 1/2 as much as than as the total donation made by Tanya and Devi. Devi donated $138 less than Tanya. How much did Mariah donate?

Solution:

Solve by Ratio method. 

In this situation, do take note that the total donation is unchanged.

T : M + D  = 2u:3u, remove u and insert the total there to become
T : M + D : T + M + D = 2 : 3 : 5 (ratio 1)

M : T + D = 1u : 2u, remove u and insert the total there to become
M : T + D : T + M + D = 1 : 2 : 3 (ratio 2)

Since total is unchanged, then we can rewrite the two ratios such as:

T : M + D : T + M + D = 6 :  9 : 15
M : T + D : T + M + D = 5 : 10 : 15

Rearrange, to find D:

D = (T + D) - T = 10u - 6u = 4u

T - D = 6u - 4u = 2u

2u = 138, u = 69

Mariah donated 5u = 5 x 69 = $345