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

cost of ribeye steak dinners = $10.36

cost of grilled salmon= $11.581

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=(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=(451.69)/(39)`

y=11.581