Question

How many pounds of candy that sells for $0.85 per lb must be mixed with candy that sells for $1.22 per lb to obtain 9 lb of a mixture that should sell for $0.92 per lb? $0.85-per-lb candy

Answer 1

Let us call x the number of lbs of $0.85 candy and y the number of lbs of $1.22 candy. The total number that x and y should add to is 9 lbs; therefore, we have

`\textcolor{#FF7968}{x+y=9}`

The amount of money x lbs of $0.85 candy and y the number of lbs of $1.22 candy make together is

`0.85x+1.22y`

This amount divided by 9 lb should give us $0.92/ lb; therefore, we have

`(0.85x+1.22y)/(9)=0.92`
`\textcolor{#FF7968}{\rightarrow0.85x+1.22y=8.28.}`

Hence, we have two equations with two unknown and all we need to do to find them is to solve the system.

The solution to the system turns out to be

`x=7.2972`
`y=1.70`

Hence, 7.2972 lb of $0.85 candy must be mixed with $1.70 lb candy to obtain a 9lb mixture that sells for $0.92 per lb.