Question

A student has some $\$1$ bills and $\$5$ bills in his wallet. He has a total of $15$ bills that are worth $\$47$. How many of each type of bill does he have?

Answer 1

Step-1: Form the system of linear equation in two variables:

Let the number of $\$1$ bills be $\mathrm{x}$ and $\$5$ bills be $\mathrm{y}$.

Then, $\mathrm{x}+\mathrm{y}=15$ $...\left(\mathrm{i}\right)$

And $\$1\mathrm{x}+\$5\mathrm{y}=\$47$

$\Rightarrow$ $\mathrm{x}+5\mathrm{y}=47$ $...\left(\mathrm{ii}\right)$

Step-2: Find the number of bills:

Subtracting $\left(\mathrm{i}\right)$ from $\left(\mathrm{ii}\right)$, we get;

$\mathrm{x}+5\mathrm{y}-\left(\mathrm{x}+\mathrm{y}\right)=47-15$

$\Rightarrow$$\mathrm{x}+5\mathrm{y}-\mathrm{x}-\mathrm{y}=32$

$\Rightarrow$ $4\mathrm{y}=32$

$\mathrm{y}=8$ [ Dividing both sides by $4$]

Now substitute $\mathrm{y}=8$ in $\left(\mathrm{i}\right)$, we get;

$\mathrm{x}+8=15$

$\Rightarrow$ $\mathrm{x}=15-8$

$\Rightarrow$ $\mathrm{x}=7$

Hence, there are $7$ bills of $\$1$ and $8$ bills of $\$5$.