Question

What is the ratio of yellow to red

6 yellow = 5 green

4 green = 3 purple

5 purple = 2 red


A.3 to 1

B.4 to 1

C.5 to 1

D.6 to 1

Answer 1

Answer: 4 to 1 (choice B)

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Step-by-step explanation:

We have 5 green in the 1st row and 4 green in the 2nd row.

The LCM is 5*4 = 20.

The ratio
`6 \text{ yellow} = 5 \text{ green}` scales up to
`24 \text{ yellow} = 20 \text{ green}` after multiplying both sides by 4.

The ratio
`4 \text{ green} = 3 \text{ purple}` scales up to
`20 \text{ green} = 15 \text{ purple}` after multiplying both sides by 5.

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These set of ratios

`6 \text{ yellow} = 5 \text{ green}\\\\4 \text{ green} = 3 \text{ purple}\\\\`

scale up to

`24 \text{ yellow} = 20 \text{ green}\\\\20 \text{ green} = 15 \text{ purple}\\\\`

The key is the "20 green" on each line. This leads to the ratios linking up.

If A = B and B = C, then A = C (transitive property).

So we can say
`24 \text{ yellow} = 20 \text{ green} = 15 \text{ purple}\\\\`

That simplifies to
`24 \text{ yellow} = 15 \text{ purple}\\\\`

We can divide both sides by 3 to get
`8 \text{ yellow} = 5 \text{ purple}\\\\`

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We now have these set of ratios

`8 \text{ yellow} = 5 \text{ purple}\\\\5 \text{ purple} = 2 \text{ red}\\\\`

Connect those two equations together to get

`8 \text{ yellow} = 2 \text{ red}\\\\`

Lastly, divide both sides by 4

`4 \text{ yellow} = 1 \text{ red}\\\\`

The ratio of yellow to red is 4 to 1.