Question

a local boys club sold 156 bags of mulch and made a total of $455 it's sold two types of mulch hard word for $3.25 a bag in Pine Box for $2.75 a bag how many bags of each kind did it sell

Answer 1

Let's define first the variables.

let H be the number of bags of the type that cost 3.25 and P the number of bags of the type that cost 2.75.

since they sold a total of 156 bags we have that H+P=156

and from the other condition we obtain 3.25H+2.75P=455

now we can solve the system of equations.

from the first equation H=156-P

substituing the previous equality in the second one we obtain:

`3.25(156-P)+2.75P=455`
`507-3.25P+2.75P=455`
`(2.75-3.25)P=-53`
`0.5P=53`
`P=106`

now that we have P, we can replace it in the first equation obtaining that H=50

then the answer will be that they sold 50 bags of $3.25 and 106 bags of $2.75