SOLUTION: at a concession stand, 7 hotdogs and 2 hamburgers cost a total of $14.50; two hot dogs and 7 hamburgers cost a total of $17.00. find the cost of one hot dog and one hamburger

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: at a concession stand, 7 hotdogs and 2 hamburgers cost a total of $14.50; two hot dogs and 7 hamburgers cost a total of $17.00. find the cost of one hot dog and one hamburger      Log On


   

Question 953251: at a concession stand, 7 hotdogs and 2 hamburgers cost a total of $14.50; two hot dogs and 7 hamburgers cost a total of $17.00. find the cost of one hot dog and one hamburger
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x=cost of hamburger; y=cost of hot dog
2x+7y=$14.50 Multiply this equation by 7.
14x+49y=$101.50
7x+2y=$17.00 Multiply this equation by 2.
14x+4y=$34.00 Subtract this from first result.
45y=$67.50 Divide each side by 45.
y=$1.50 ANSWER 1: hot dogs cost $1.50.
7x+2y=$17.00 Plug in y
7x+2($1.50)=$17.00
7x+$3.00=$17.00
7x=$14.00
x=$2.00 ANSWER 2: Hamburgers cost $2.00.
CHECK:
2x+7y=$14.50
2($2.00)+7($1.50)=$14.50
$4.00+$10.50=$14.50
$14.50=$14.50