The band is selling wrapping paper for a fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. The band sold a total of 55 rolls and made $950. If a roll of plain wrapping paper cost $14 and a roll of shiny cost $20, how many rolls of each did they sell ?
Accepted Solution
A:
x= # plain rolls y= # shiny rolls
QUANTITY EQUATION: x+y=55
COST EQUATION: $14x + $20y= $950
SOLVE: Solve for one variable in quantity equation. Substitute that answer in cost equation.
STEP 1: x+y=55 subtract y from both sides x= 55-y
STEP 2: $14x + $20y= $950 14(55-y) + 20y= 950
multiply 14 by all in parentheses (14*55)+(14*-y) + 20y= 950 770-14y+20y= 950
combine like terms 770+6y= 950
subtract 770 from both sides 6y= 180
divide both sides by 6 y= 30 shiny rolls
STEP 3: Substitute y answer in either equation to solve for x.
x+y=55 x+30=55 subtract 30 from both sides x= 25 plain rolls