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

Answer:

20:35:91

Step-by-step 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

$7x=5y\\ \\y=\dfrac{7}{5}x.$

4. Now,

$a=4x\\ \\b=7x\\ \\c=13\cdot \dfrac{7}{5}x=\dfrac{91}{5}x,$

so

$a:b:c=4x:7x:\dfrac{91}{5}x\\ \\a:b:c=20:35:91$