You buy 4 bags of sand and 3 bags of pea gravel for $24. In a second purchase (at the same prices), you buy 2 bags of sand for $6. X=Sand Y=Pea Gravel. How much does a bag of sand cost? How much does a bag of Pea Gravel Cost?

Sand is $3 per bag and pea gravel is $4 per bag.

This is an example of solving two equations in two unknowns. Each purchase must be "translated" into an equation:

If we use X for the sand and Y for the pea gravel, the two purchases can be written as

##4X+3Y=24## and

##2X=6##

The second equation simplifies (divide each side by 2) into

##X=3##

so, sand is $3 per bag.

Now, place this value into the other equation:

##4(3)+3Y=24##

##12+3Y=24## (subtract 12 from each side to "collect like terms")

##3Y=12##

##Y=4##

Pea gravel is $4 per bag.