SOLUTION: At a concession stand, five hotdogs and two hamburgers cost $10.25; two hotdogs and five hamburgers cost $12.50. How much does one hotdog cost? Thank you very much for your hel

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Question 734854: At a concession stand, five hotdogs and two hamburgers cost $10.25; two hotdogs and five hamburgers cost $12.50. How much does one hotdog cost?
Thank you very much for your help!
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!
let hotdogs be and hamburgers
if five hotdogs and two hamburgers cost $, then
.....eq.1
if two hotdogs and five hamburgers cost $,then
.....eq.2
now solve this system:

.....eq.1
.....eq.2
______________________________
.....eq.1....solve for

......plug it in eq.2

.....eq.2..solve for

........hamburger cost
now find

.....hotdog cost

check:
.....eq.1

.....eq.2

Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
Let x = cost of hot dog, y = cost of hamburger,
we have
5x + 2y = 10.25 and
2x + 5y = 12.50
we need to know the value for x
solve the second equation for y and we have
y = (12.50 - 2x) / 5 = 2.50 - 2x/5
now we substitute for y in our first equation,
5x + 2 (2.50 - 2x/5) = 10.25 combining like terms,
5x + 5.00 - 4x/5 = 10.25 and
5x - 4x/5 = 5.25 and
25x - 4x = 26.25 and 21x = 26.25
x = $1.25, so the hot dog costs $1.25