Question

Tom had 47 Portugal's which he shared with his 2 friends Ryan and Neil. He gave Neil 3 less than Ryan and kept 5 more than Ryan. Calculate how many portugals Tom kept for himself

Answer 1

Let t be how many he kept, r how many he gave to Ryan and n how many he gave to Neil.

The total have to still be 47, so:

`t+r+n=47`

If he gave Neil 3 less than Ryan, than the number he gave to Neil plus 3 will be the number he gave to Ryan, so:

`n+3=r`

And if he kept 5 mre than Ryan, the number he kept is equal the number he gave Ryan plus 5:

`t=r+5`

Since we want to know the number he kept, t, we can substitute the other variables so that we have an equation with only the variable t.

So, since r is in all equations, let's first solve the second for n and substitute it into the first, which will reduce the system to only 2 variables:

`\begin{gathered} n+3=r \\ n=r-3 \end{gathered}`
`\begin{gathered} t+r+n=47 \\ t+r+r-3=47 \\ t+2r=50 \end{gathered}`

Now, we can solve the third equation for r and substitute it into the above one:

`\begin{gathered} t=r+5 \\ r=t-5 \end{gathered}`
`\begin{gathered} t+2r=50 \\ t+2(t-5)=50 \\ t+2t-10=50 \\ 3t=60 \\ t=(60)/(3) \\ t=20 \end{gathered}`

So, Tom kept 20 for himself.