Question

4. A cash register contains $10 bills and $50 bills with a total value of $1080. If there are 28 bilistotal, then how many of each does the register contain?

Answer 1

we can write 2 equations from the statements

1. contains $10 bills and $50bills with a total value of $1080

`10x+50y=1080`

where x is the number of bills of $10 and y the bills of $50

2. if there are 28 bills

`x+y=28`

then we can use any method to find the values of x and y

i will use elimination, for it i will multiply the second equation by 10 and do a substract to eliminate x

`\begin{gathered} 10x+10y=10*28 \\ 10x+10y=280 \end{gathered}`
`\begin{gathered} 10x+50y=1080- \\ 10x+10y=280 \\ ------------- \\ 0x+40y=800 \end{gathered}`

the new equation is

`40y=800`

we can solve x from it

`\begin{gathered} y=(800)/(40) \\ y=20 \end{gathered}`

so, the number of bills of $50 is 20

I must replace y on any equation to find x(I will use the second equation)

`\begin{gathered} x+y=28 \\ x+20=28 \\ x=28-20 \\ x=8 \end{gathered}`

so, the number of bills of $10 is 8