[CA]: ( $7$ . $3$ - $7$ . $5$ $7$ . $7$ ) $\newline$ possible $\newline$ A waitress sold $20$ ribeye steak dinners and $12$ grilled salmon dinners, totaling $\$ 573.12$ on a particular day. Another day she sold $26$ ribeye steak dinners and $6$ grilled salmon dinners, totaling $\$ 582.07$ . How much did each type of dinner cost? $\newline$ $\square$ and the cost of salmon dinners is $\$$ $\square$ The cost of ribeye steak dinners is $\$$ $\square$ (Simplify your answer. Round to the nearest hundredth as needed.)

Full solution

Q. [CA]: (

7

3

7

5

7

7

)

\newline

possible

\newline

A waitress sold

20

ribeye steak dinners and

12

grilled salmon dinners, totaling

\$ 573.12

on a particular day. Another day she sold

26

ribeye steak dinners and

6

grilled salmon dinners, totaling

\$ 582.07

. How much did each type of dinner cost?

\newline

\square

and the cost of salmon dinners is

\$

\square

The cost of ribeye steak dinners is

\$

\square

(Simplify your answer. Round to the nearest hundredth as needed.)

Define Variables: Let's call the cost of a ribeye steak dinner $r$ and the cost of a grilled salmon dinner $s$ . We have two equations based on the information given: $20r + 12s = 573.12$ ( $1$ ) $26r + 6s = 582.07$ ( $2$ )
Multiply Equation: Multiply equation ( $2$ ) by $2$ to make the coefficient of ＂s＂ the same as in equation ( $1$ ): $\newline$ $2(26r + 6s) = 2(582.07)$ $\newline$ $52r + 12s = 1164.14 \quad (3)$
Subtract Equations: Subtract equation ( $1$ ) from equation ( $3$ ) to eliminate ＂s＂: $\newline$ $(52r + 12s) - (20r + 12s) = 1164.14 - 573.12$ $\newline$ $32r = 591.02$
Solve for r: Divide both sides by $32$ to solve for ＂r＂: $\newline$ $r = \frac{591.02}{32}$ $\newline$ $r = 18.47$
Substitute and Solve for s: Now substitute the value of $r$ back into equation ( $1$ ) to solve for $s$ : $\newline$ $20(18.47) + 12s = 573.12$ $\newline$ $369.4 + 12s = 573.12$
Isolate $s$ : Subtract $369.4$ from both sides to isolate $s$ : $12s = 573.12 - 369.4$ $12s = 203.72$
Final Solution: Divide both sides by $12$ to solve for ＂s＂: $\newline$ $s = \frac{203.72}{12}$ $\newline$ $s = 16.98$