The community relief fund receives a large donation of $2800. the foundation agrees to spend the money on $20 school bags, $25 sweaters, $5 books. they want to buy 200 items and send them to schools in earthquake-hit areas. they must order as many books as school bags and sweaters combined. how much of each must they buy?

The foundation should buy 40 school bags, 60 sweaters and 100 books.

Step-by-step explanation:

Let x be the number of school bags, y - the number of sweaters and z - the number of books the foundation wants to buy. They must order as many books as school bags and sweaters combined, so

z = x + y

1 school bag costs $20, then x bags cost $20x,

1 sweater costs $25, then y sweaters cost $25y,

1 book costs $5, then z books cost $5z.

The foundation wants to buy 200 items, then

x + y + z = 200

The foundation wants to spend $2,800, so

20x + 25y + 5z = 2,800

We get the system of three equations:

Substitute the first equation into the last two equations:

From the first equation

Substitute it into the second equation

They should buy 40 school bags, 60 sweaters and 100 books.