Question

A waitress sold 12 ribeye steak dinners and 39 grilled salmon totaling $575.53 on a particular day. Another day she sold 25 ribeye steak dinners and 13 grilled salmon dinners, totaling $582.43. How much did each type of dinner cost?

Answer 1

Answer:

cost of ribeye steak dinners = $10.36

cost of grilled salmon= $11.581

Step-by-step explanation:

Let the cost of one steak dinners be x

Let the cost of one  grilled salmon be y

One a particular day the waitress sells  12 ribeye steak dinners and 39 grilled salmon for a total is $575.53 which can be written in equation as

12(x)+39(y)= $575.53-------------------------------------(1)

On another day she sells  25 ribeye steak dinners and 13 grilled salmon dinners  totals to $582.43.This can be represented  as

25(x)+ 13(y)= $582.43-------------------------------------(2)

solving the equation (1) and (2)

eq(1) x 1$12x+39y= 575.53$

eq(2) x 3$125x+ 39y= 1747.29$-------------------------(3)

Subtracting these equation we get,

$113x=1171.76$

$x=\frac{1171.76}{113}$

x= 10.36

Now  substituting this in equation (1)

$12(10.36)+39(y)= 575.53$

$123.84+39y=575.53$

$39y=575.53 - 123.84$

$y=\frac{451.69}{39}$

y=11.581