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A waitress sold 10 ribeye steak dinners and 30 grilled salmon dinners, totaling
$583.22 on a particular day. Another day she sold 22 ribeye steak dinners and 15 grilled salmon dinners, totaling
$580.18. How much did each type of dinner cost?
The cost of ribeye steak dinners is
$
◻ and the cost of salmon dinners is
$
◻
◻. (Simplify your answer. Round to the nearest hundredth as needed.)
this
View an example
Get more help
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Clear all
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A waitress sold $10$ ribeye steak dinners and $30$ grilled salmon dinners, totaling $\$ 583.22$ on a particular day. Another day she sold $22$ ribeye steak dinners and $15$ grilled salmon dinners, totaling $\$ 580.18$ . How much did each type of dinner cost? $\newline$ The cost of ribeye steak dinners is $\$$ $\square$ and the cost of salmon dinners is $\$$ $\square$ $\square$ . (Simplify your answer. Round to the nearest hundredth as needed.) $\newline$ this $\newline$ View an example $\newline$ Get more help $\cdot$ $\newline$ Clear all $\newline$ Check answer

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Percent error: word problems

Full solution

Q. A waitress sold

10

ribeye steak dinners and

30

grilled salmon dinners, totaling

\$ 583.22

on a particular day. Another day she sold

22

ribeye steak dinners and

15

grilled salmon dinners, totaling

\$ 580.18

. How much did each type of dinner cost?

\newline

The cost of ribeye steak dinners is

\$

\square

and the cost of salmon dinners is

\$

\square

\square

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

\newline

this

\newline

View an example

\newline

Get more help

\cdot

\newline

Clear all

\newline

Check answer

Define Variables: Let's call the cost of one ribeye steak dinner $R$ and the cost of one grilled salmon dinner $S$ .
First Day Equation: From the first day, we have the equation $10R + 30S = 583.22$ .
Second Day Equation: From the second day, we have the equation $22R + 15S = 580.18$ .
Multiply First Equation: Let's multiply the first equation by $2$ to help eliminate one of the variables, so we get $20R + 60S = 1166.44$ .
Multiply Second Equation: Now, let's multiply the second equation by $4$ to get $88R + 60S = 2320.72$ .
Eliminate Variable S: Subtract the modified first equation from the modified second equation to eliminate S: $88R + 60S - (20R + 60S) = 2320.72 - 1166.44$ .
Solve for R: This simplifies to $68R = 1154.28$ .
Calculate R: Divide both sides by $68$ to find $R$ : $R = \frac{1154.28}{68}$ .
Substitute $R$ in First Equation: Calculating $R$ gives us $R = 16.97$ .
Solve for S: Now, substitute $R$ back into the first equation: $10(16.97) + 30S = 583.22$ .
Correct Calculation for S: This simplifies to $169.7 + 30S = 583.22$ .
Correct Calculation for S: This simplifies to $169.7 + 30S = 583.22$ . Subtract $169.7$ from both sides to solve for $S$ : $30S = 583.22 - 169.7$ .
Correct Calculation for S: This simplifies to $169.7 + 30S = 583.22$ . Subtract $169.7$ from both sides to solve for $S$ : $30S = 583.22 - 169.7$ . Calculating gives us $30S = 413.52$ .
Correct Calculation for S: This simplifies to $169.7 + 30S = 583.22$ . Subtract $169.7$ from both sides to solve for S: $30S = 583.22 - 169.7$ . Calculating gives us $30S = 413.52$ . Divide both sides by $30$ to find S: $S = 413.52 / 30$ .
Correct Calculation for S: This simplifies to $169.7 + 30S = 583.22$ . Subtract $169.7$ from both sides to solve for S: $30S = 583.22 - 169.7$ . Calculating gives us $30S = 413.52$ . Divide both sides by $30$ to find S: $S = 413.52 / 30$ . Calculating S gives us $S = 13.78$ .
Correct Calculation for S: This simplifies to $169.7 + 30S = 583.22$ . Subtract $169.7$ from both sides to solve for $S$ : $30S = 583.22 - 169.7$ . Calculating gives us $30S = 413.52$ . Divide both sides by $30$ to find $S$ : $S = 413.52 / 30$ . Calculating $S$ gives us $S = 13.78$ . But wait, there's a mistake in the calculation of $S$ . Let's correct it: $S$ should be $169.7$ $2$ , which rounds to $169.7$ $3$ .

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