A student bought 1 box of crayons and 5 reams of paper for $54. She bought 5 boxes of crayons and 3 reams of paper for $50. What is the cost of each box of crayons and each ream of paper?

1 box of crayons costs $4.00 1 ream of paper costs $10.00

Two unknowns and two equations thus solvable.

Let 1 box of crayons cost be ##c## Let 1 ream of paper cost be ##p##

condition(1): ##->1c+5p=54" "## written as ##c+5p=54##

condition(2): ##->5c+3p=50## '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From condition(1)

Subtract ##5p## from both sides.

##c=54-5p##

Substitute for ##c## in condition(2) giving:

##color(brown)(5c+3p=50)color(blue)(" "->" "5(54-5p)+3p=50)##

##270-25p+3p=50##

##270-22p=50##

Subtract 270 from both sides

##0-22p=-220##

Multiply both sides by (-1)

##22p=220##

divide both sides by 22

##color(magenta)(p=10)## '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Substitute for ##p=10## in condition(1)

##color(brown)(c+5p=54)color(blue)(" "->" "c+5(10)=54)##

##c+50=54##

##color(magenta)(c=4)##