Question

There are between 50 and 60 number of eggs in a basket. When Loza counts by 3's, there are 2 eggs left over. When she counts by 5's, there are 4 left over. How many eggs are there in the basket?

Answer 1

Total Number of eggs in the basket = 59

Explanation:

The n be number of eggs and n is between 50 and 60.

So, the possible outcomes are 50, 51, 52, .... , 59 and 60.

If the eggs are counted in 5's, the left over eggs are 4.

Hence, the number of eggs is NOT COMPLETELY DIVISIBLE by 5

So, n ≠ 50, 55 and 60.

If the eggs are counted in 3's the leftover eggs are 2.

Hence, the number of eggs is NOT COMPLETELY DIVISIBLE by 3

n ≠ 51, 54, 57 and 60.

Now, the possible values of n = 52, 53, 56, 58 and 59.

Checking for 52, when counted in 5, left over eggs are 2(as 5 x 10=50)

Checking for 53, when counted in 5, left over eggs are 3(as 3 x 10=50)

Checking for 56, when counted in 5, left over eggs are 1

Checking for 58, when counted in 5, left over eggs are 3

Checking for 59, when counted in 5, left over eggs are 4 and when counted in 3, left over eggs are 2.

Hence, TOTAL NUMBER OF EGGS IN THE BASKET ARE 59 as it satisfies bot the given conditions.

Answer 2

The number of eggs in the basket is 56

Explanation:

Given as :

Let The number of eggs in the basket = 3x + 5x

When Loza counts 3's , there are 2 eggs left over

I.e , 3 ( x - 2 )

And When Loza counts 5's , there are 4 eggs left over

I.e 5 ( x - 4 )

∴ 3 x - 6 = 5 x - 20

Or, 20 - 6 = 5 x - 3 x

Or, 14 = 2 x

∴ x = 7

So, the number of eggs = 3 × 7 + 5 × 7

= 21 + 35 = 56

Hence The number of eggs in the basket is 56 Answer