Question

A bank teller has a total of 35 bills, made up of $5 bills and $10 bills. If the total value of the money is $200, how many bills of each denomination does she have?

Answer 1

Answer:

The bank teller has 30 $5-bills and 5 $10-bills.

Explanation:

• Let the number of $5 bills = x

,

• Let the number of $10 bills = y

The bank teller has a total of 35 bills.

$\implies x+y=35\cdots(1)$

The total value of the money is $200.

$\begin{gathered} \text{The value of x \ 5 bills = 5x} \\ \text{The value of y \ 10 bills = 10y} \\ \implies5x+10y=200\cdots(2) \end{gathered}$

We can divide equation (2) all through by 5:

$\begin{gathered} \frac{5x}{5}+\frac{10y}{5}=\frac{200}{5} \\ x+2y=40\cdots(3) \end{gathered}$

Solve equations (1) and (3) simultaneously:

$\begin{gathered} x+2y=40\cdots(3) \\ x+y=35\cdots(1) \\ \text{Subtract } \\ y=5 \end{gathered}$

Solve for x:

$\begin{gathered} x+y=35 \\ x+5=35 \\ x=35-5 \\ x=30 \end{gathered}$

x=30 and y=5

Thus, the bank teller has 30 $5-bills and 5 $10-bills.