At a concession stand, five hot dog left parenthesis s right parenthesis and four hamburger left parenthesis s right parenthesi
s cost $12.00 ; four hot dog left parenthesis s right parenthesis and five hamburger left parenthesis s right parenthesis cost $12.75 . find the cost of one hot dog and the cost of one hamburger .
5 hotdogs + 4 hamburgers = $12.00 4 hotdogs + 5 hamburgers = $12.75 hotdogs = x hamburgers = y
5x + 4y = 12 4x + 5y = 12.75 subtract the second equation from the first: (5x + 4y = 12) - (4x + 5y = 12.75) = 1x - 1y = -0.75 x + 0.75 = y ( this means one hotdog plus $0.75 equals one hamburger) now substitute "y" for "x + 0.75" in either equation to find x ( I used the first equation) 5x + 4y = 12 5x + 4( x + 0.75) = 12 5x + 4x + 3 = 12 9x + 3 = 12 9x = 9 x = 1 ( one hotdog costs $1.00) now substitute 1 for "x" in either equation to find y ( I used the first equation again) 5x + 4y = 12 5(1) + 4y = 12 5 + 4y = 12 4y = 7 y = 1.75 ( one hamburger costs $1.75)
checking answers with either equation ( input $1.00 for hotdogs and $1.75 for hamburgers): equation 1: 5 hotdogs + 4 hamburgers = $12.00 5($1.00) + 4($1.75) = $12.00 $5.00 + $7.00 = $12.00 $12.00 = $12.00 ✔
