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

Answer:

56 eggs

Step-by-step explanation:

If $\frac{2}{7}$ of all eggs are green, $\frac{1}{4}$ of all are blue, then

$1-\dfrac{2}{7}-\dfrac{1}{4}=\dfrac{28-2\cdot 4-7}{28}=\dfrac{13}{28}$

of all eggs are red.

We know that there are 26 red eggs

$26\text{ eggs }-\dfrac{13}{28}\\ \\x\text{ eggs }- 1[=\dfrac{28}{28}]$

Make a proportion

$\dfrac{26}{x}=\dfrac{\frac{13}{28}}{1}\\ \\26\cdot 1=x\cdot \dfrac{13}{28}\ [\text{Cross multiply}]\\ \\13x=26\cdot 28\ [\text{Multiply by 28 to get rid of fraction}]\\ \\x=\dfrac{26\cdot 28}{13}\ [\text{Divide by 13 to get x}]\\ \\x=2\cdot 28\\ \\x=56$