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 [tex]t[/tex]≡[tex]3(mod4)[/tex]
We also know that [tex]t[/tex]≡[tex]4(mod 5)[/tex]
Between 10 and 20, there are only 2 numbers t≡[tex]4(mod 5)[/tex], these numbers are 14 and 19.
However, 14≡[tex]2(mod 4)[/tex] so it doesn't add up.
On the other hand, 19 ≡3[tex](mod4)[/tex] and therefore, this is the answer.
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.
[tex]n\equiv 3(mod4)[/tex] ... (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.
[tex]n\equiv 4(mod5)[/tex] ... (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.
