Question

[Q1]

White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 3:7
The ratio of the number of white circles to the number of white squares is 4:5
The ratio of the number of black circles to the number of black squares is 2:5
Work out what fraction of all the shapes are circles.

Answer 1

Hi,

Explanation:

Let's n the number of shapes.

Using ratio 3:7, n must be divisible by 3+7=10

Using ratio 4:5, n must be divisible by 4+5=9

Using ratio 2:5, n must be divisible by 2+5=7

n must be multiple of 10*9*7=630

`\begin{array}c&white&black&total\\-----&-----&-----&-----\\Circles&84&126&441\\Squares&105&315&420\\-----&-----&-----&-----\\total&189&441&630\\\\\end{array}\\\\\\fraction\ = (circles)/(shapes) =(441)/(630) =\boxed{(7)/(10) }`