Question

Fifteen (15) boys went for fruit hunting at Achimota forest on a weekend. They got a certain number (n) of mangoes at the end of their hunting and decided to share it equally. When they divided the (n) mangoes, the remainder was 10. What would have been the remainder if the same (n) mangoes were divided by 7 boys instead of the 15 boys

Answer 1

The remainder would be -6 if the same (n) mangoes were divided by 7 boys instead of 15 boys.

Step-by-step explanation:

To find the remainder if the same (n) mangoes were divided by 7 boys instead of 15 boys, we need to find the value of (n) first.

We know that when the (n) mangoes are divided by 15 boys, the remainder is 10. This can be represented as:

(n / 15) = q + (10 / 15), where q is the quotient.

We can simplify this equation to:

(n / 15) = q + (2 / 3)

Multiplying both sides by 15, we get:

n = 15q + 10

To find the remainder if the same (n) mangoes are divided by 7 boys, we substitute n = 15q + 10 into the equation:

(15q + 10) / 7 = q2 + (r / 7), where q2 is the new quotient and r is the new remainder.

We can simplify this equation to:

2q + (4 / 7) = q2 + (r / 7)

Multiplying both sides by 7, we get:

14q + 4 = 7q2 + r

Now we need to find the value of r. To do this, we can use the fact that n = 15q + 10:

14q + 4 = 7q2 + (15q + 10)

Simplifying this equation, we get:

14q + 4 = 7q2 + 15q + 10

Subtracting 14q from both sides, we get:

4 = 7q2 + q + 10

Subtracting 10 from both sides, we get:

-6 = 7q2 + q

The remainder is -6 when the same (n) mangoes are divided by 7 boys instead of 15 boys.