Question

Sue's Sushi placed two orders with its fish supplier. One order was for 15 pounds of salmon and 8 pounds of tuna; the order totaled $259. The other order was for 12 pounds of salmon and 6 pounds of tuna; this order totaled $204. What is the cost for one pound of salmon and one pound of tuna?

Answer 1

x= salmon cost per pound
y= tuna cost per pound

$15x + $8y= $259
$12x + $6y= $204

Solve for one variable in one equation and substitute it in the other equation.

15x + 8y= 259
subtract both sides by 8y
15x= 259 - 8y
divide both sides by 15
x=(259-8y)/15

Substitute in second equation

12x + 6y= 204
12((259-8y)/15) + 6y= 204
multiply everything by 15 to eliminate fraction

(15)(12(259-8y)/15) + (15)(6y)= (204)(15)
(12*259) + (12*-8y) + 90y= 3060
multiply inside parentheses

3108 - 96y + 90y= 3060
combine like terms & subtract 3108 from both sides

-6y= -48
divide both sides by -6

y= $8 cost of tuna per pound

Substitute y=8 in either equation
15x + 8y= 259
15x + 8(8)= 259
15x + 64= 259
15x= 195
x= $13 cost of salmon per pound

CHECK:
12x + 6y= 204
12(13) + 6(8)= 204
156 + 48= 204
204= 204

ANSWER: One pound of salmon costs $13 and one pound of tuna costs $8.

Hope this helps! :)