Originally Posted by
Soroban Hello, magentarita!
Let $\displaystyle x$ = number of 1p coins.
Let $\displaystyle y$ = number of 5p coins.
We are told that: .$\displaystyle x \:=\:3y+1 \quad\Rightarrow\quad x - 3y \:=\:1$ .[1]
The total value is: .$\displaystyle 1\!\cdot\!x + 5\!\cdot\!y \:=\:145 \quad\Rightarrow\quad x + 5y \:=\:145$ .[2]
Subtract [1] from [2]: .$\displaystyle 8y \:=\:144 \quad\Rightarrow\quad y \:=\:18$
Substitute into [1]: .$\displaystyle x - 3(18) \:=\:1\quad\Rightarrow\quad x \:=\:55$
Answer: .$\displaystyle \begin{Bmatrix}55\,\text{ 1p coins} \\ 18\,\text{ 5p coins} \end{Bmatrix}$