Question

1. Comet, Astro, and Pepper are puppies. The ratio of Comet’s weight to Astro’s weight is 5:4. The ratio of Astro’s weight to Pepper’s weight is 4:3. Comet weighs 50 pounds. How much do they weight altogether?



2. A board is painted yellow, black, and gray in the ratio 5:3:2. The section of the board that is painted yellow is 40 inches long. What is the length of the board?

Answer 1

C : A = 5 : 4 = 5x : 4x
but C = 50
5x = 50
x = 10, then 4x = 40

A : P = 4 : 3 = 4y : 3y
but 4y = 40, so y = 10 and 3y = 30
their total weight = 50+40+30 = 120

or:
since
C : A = 5:4 and A : P = 3 : 3
C : A : P = 5 : 4 : 3 or 5k : 4k : 3k
(I could only do that because the "connecting" term between the
ratios was the same, namely 4)
so 5k = 50
k = 10
total is 12k or 120

2. very simple
y : b : g = 5:3:2 or 5x:3x:2x
y = 5x = 40
x = 8
then how long is the board??
Isn't it 10x ?