Question

An Easter basket contains eggs of three different colors. Find the total number of eggs in the basket if 2 7 of all eggs are green, 1 4 of all are blue and the rest 26 eggs are red.

Answer 1

56 eggs

Explanation:

If
`(2)/(7)` of all eggs are green,
`(1)/(4)` of all are blue, then

`1-(2)/(7)-(1)/(4)=(28-2\cdot 4-7)/(28)=(13)/(28)`

of all eggs are red.

We know that there are 26 red eggs

`26\text{ eggs }-(13)/(28)\\ \\x\text{ eggs }- 1[=(28)/(28)]`

Make a proportion

`(26)/(x)=((13)/(28))/(1)\\ \\26\cdot 1=x\cdot (13)/(28)\ [\text{Cross multiply}]\\ \\13x=26\cdot 28\ [\text{Multiply by 28 to get rid of fraction}]\\ \\x=(26\cdot 28)/(13)\ [\text{Divide by 13 to get x}]\\ \\x=2\cdot 28\\ \\x=56`