Question

The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 8 type A widgets is equal to the weight of 3 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?

Answer 1

Answer:$\frac{77}{96}$

Step-by-step explanation:

Given

weight of 8 Type A widget is equal to weight of 3 type B widgets

i.e. 8A=3B  (Let's say)

$A=\frac{3}{8}B$

Also

Weight of 5 Type B widgets is equal to the weight of 7 type C widgets

i.e.

5B=7C

$C=\frac{5}{7}B$

ratio of total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget

$\frac{A+B}{B+C}=\frac{\frac{3}{8}B+B}{B+\frac{5}{7}}$

$=\frac{11\times 7}{8\times 12}=\frac{77}{96}$