Question

A family member has some five dollar Bill's and one dollar Bill's in her wallet.Although she has 18 Bill's and a total of 62.How many of each bill does she have?

Answer 1

Step-by-step explanation:

x: amount of five dollar bills

y: amount of one dollar bills

The sum of the amounts of each kind of bills is 18 and the sum of the value of all bills is 62. We can write a system of equations:

`\begin{cases}x+y=18 \\ 5x+y=62\end{cases}`

And we can solve using the elimination method. Substracting the first equation from the second:

`\begin{gathered} 5x+y=62 \\ - \\ x+y=18 \\ \text{ --------------} \\ (5x-x)+(y-y)=62-18 \\ 4x=44 \end{gathered}`

Solving for x:

`x=(44)/(4)=11`

WIth x = 11 we can replace into the first equation and solve for y:

`\begin{gathered} 11+y=18 \\ y=18-11=7 \end{gathered}`

Answers:

She has:

• 11 five dollar bills

,

• 7 one dollar bills