Question

If a: b = 2:3, b: c = 4:3, and c: d = 7: 8, find a: d.

Answer 1

Answer:

a:d=7:9

Step-by-step explanation:

We have a system with 3 equation:

$\frac{a}{b}=\frac{2}{3}\\\frac{b}{c}=\frac{4}{3}\\\frac{c}{d}=\frac{7}{8}$

If we multiply all of these equations, then we have:

$\frac{a}{b}*\frac{b}{c}*\frac{c}{d}=\frac{2}{3}*\frac{4}{3}*\frac{7}{8}\\\frac{a*b*c}{b*c*d}=\frac{2*4*7}{3*3*8}\\\frac{a}{d}=\frac{56}{72}$

If we simplify this fraction dividing by 9, then:

$\frac{a}{d}=\frac{56:9}{72:9}=\frac{7}{9}$

Therefore, a:d=7:9