Question

Yusuf has between 10 and 20 toffees. If he counts his toffees in 4s, he has 3 left over. If he counts his toffees in 5s, he has 4 left over. How many toffees has Yusuf got?

Answer 1

Answer:

19 toffees.

Step-by-step explanation:

It is given that Yusuf has between 10 and 20 toffees.

Let n be the number of toffees.

If he counts his toffees in 4s, he has 3 left over.

$n\equiv 3(mod4)$      ... (1)

So, the possible values of n between 10 and 20 are 11, 15 and 19.

If he counts his toffees in 5s, he has 4 left over.

$n\equiv 4(mod5)$       ... (2)

So, the possible values of n between 10 and 20 are 14 and 19.

From (1) and (2) the possible value of n between 10 and 20 is 19.

Therefore, Yusuf has 19 toffees.

Answer 2

Answer:

Yusuf got 19 toffees

Step-by-step explanation:

The problem tells us that if Yusuf counts his toffees in 4's, he has 3 left. Let's call the number of toffees "t", then we know that $t$≡$3(mod4)$

We also know that $t$≡$4(mod 5)$

Between 10 and 20, there are only 2 numbers t≡$4(mod 5)$, these numbers are 14 and 19.

However, 14≡$2(mod 4)$ so it doesn't add up.

On the other hand, 19 ≡3$(mod4)$ and therefore, this is the answer.