Question

A waitress sold 16 ribeye steak dinners and 26 grilled salmon​dinners, totaling ​$596.12 on a particular day. Another day she sold 28 ribeye steak dinners and 13 grilled salmon​ dinners, totaling ​$584.01 . How much did each type of dinner​ cost? (Round to the nearest hundredth as​ needed.)
A. What is the cost of ribeye steak dinners?
B. what is the cost of salmon dinners?

Answer 1

Answer:

(A) $14.30

(B) $14.13

Step-by-step explanation:

Let x represent cost of each ribeye steak dinner and y represent cost of each grilled salmon ​dinner.

(B) We have been given that a waitress sold 16 ribeye steak dinners and 26 grilled salmon​dinners, totaling ​$596.12 on a particular day. We can represent this information in an equation as:

$16x+26y=596.12...(1)$

We are also told that another day she sold 28 ribeye steak dinners and 13 grilled salmon​ dinners, totaling ​$584.01. We can represent this information in an equation as:

$28x+13y=584.01...(2)$

Now, we will use substitution method to solve our system of linear equations. From equation (1), we will get:

$x=\frac{596.12-26y}{16}$

Upon substituting this value in equation (2), we will get:

$28(\frac{596.12-26y}{16})+13y=584.01$

$1.75(596.12-26y)+13y=584.01$

$1043.21-45.5y+13y=584.01$

$1043.21-32.5y=584.01$

$-32.5y=584.01-1043.21$

$-32.5y=-459.2$

$y=\frac{-459.2}{-32.5}$

$y=14.12923\approx 14.13$

Therefore, cost of each grilled salmon ​dinner is $14.13.

(A) To find the cost of each ribeye dinner, we will substitute $y=14.12923$ in equation $x=\frac{596.12-26y}{16}$.

$x=\frac{596.12-26(14.12923)}{16}$

$x=\frac{596.12-367.35998}{16}$

$x=\frac{228.76002}{16}$

$x=14.29750125\approx 14.30$

Therefore, the cost of ribeye steak dinners is $14.30.