Question

Given a:b and b:c, find a:b:c. Write the ratio in simplest form. a:b=4:7 and b:c=5:13 need help

Answer 1

20:35:91

Explanation:

Given:

`a:b=4:7\\ \\b:c=5:13`

Find:

`a:b:c`

1. Since
`a:b=4:7,` then

`a=4x\\ \\b=7x`

2. Since
`b:c=5:13,` then

`b=5y\\ \\c=13y`

3. We have
`b=7x` and
`b=5y,` so

`7x=5y\\ \\y=(7)/(5)x.`

4. Now,

`a=4x\\ \\b=7x\\ \\c=13\cdot (7)/(5)x=(91)/(5)x,`

so

`a:b:c=4x:7x:(91)/(5)x\\ \\a:b:c=20:35:91`