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:

Total number of eggs in basket = 56

Step-by-step explanation:

Let z be the total number of eggs

Green eggs = $\frac{2}{7}$ × z   ........1

Blue eggs =  $\frac{1}{4}$ × z    .......2

Rest of eggs = 26  ........3

The addition of 1, 2 and 3 is equal to z  

$\frac{2}{7}$ × z + $\frac{1}{4}$ + 26 = z

$\frac{8z + 7 z}{28}$ + 26 = z                        ∵GCF for 4 and 7 is 28  

$\frac{15z}{28}$  + 26 = z

15z + (26 × 28) = 28z                ∵ multiply both sides by 28

15z + 728 = 28z

28z - 15z = 728     .......... rearranging above equation

13z = 728  ⇒   z = $\frac{728}{13}$   ⇒  z = 56

Total number of eggs = z = 56

Answer 2

Answer:  There are total 56 eggs in the basket.

Step-by-step explanation:  Given that an Easter basket contains eggs of three different colors, out of which $\dfrac{2}{7}$ are green, $\dfrac{1}{4}$ are blue and rest 26 eggs are red.

We are to find the total number of eggs in the basket.

Let x be the total number of eggs in the Easter basket.

Then, according to the given information, we have

$\dfrac{2}{7}\times x+\dfrac{1}{4}\times x+26=x\\\\\\\Rightarrow \dfrac{8x+7x}{28}+26=x\\\\\\\Rightarrow \dfrac{15x}{28}+26=x\\\\\\\Rightarrow x-\dfrac{15x}{28}=26\\\\\\\Rightarrow \dfrac{28x-15x}{28}=26\\\\\\\Rightarrow \dfrac{13x}{28}=26\\\\\Rightarrow x=\dfrac{26\times 28}{13}\\\\\Rightarrow x=56.$

Thus, there are total 56 eggs in the basket.