A waitress sold 12 ribeye steak dinners and 30 grilled salmon dinners, totaling $557.59 on a particular day. Another day she sold 21 ribeye steak dinners and 10 grilled salmon dinners, totaling $582.75 . How much did each type of dinner cost?
Ribeye steak = x
Grilled salmon = y
On the first scenario:
12x + 30y = 557.59
In the second scenario:
21x + 10y = 582.75
If we multiply our second equation by 3, we get:
63x + 30y = 1748.25
We can then subtract our first equation from this new equation, to get:
51x = 1748.25-557.59 = 1190.66
x = $23.34627450980392
Plugging this into our first equation, we get:
280.1552941176470 + 30y = 557.59
30y = 277.434705882353
y = $9.24782352941177
The ribeye steak dinner is then $23.34627450980392, and the Grilled salmon is $9.24782352941177
If the answer is in dollars, shouldn't you round the nearest hundredth?
not if the question doesn't say to do so... for all we know the question wants the exact value in dollars
Imagine a waiter saying the bill is $23.34627450980392, and the next thing you know, you're trying to cut a penny.
Why must I imagine this scenario? Aren't we only looking at what's given in the problem, not anything outside of it? Imagine if I asked you to solve for the volume of a pyramid, and then saying "wait, in real life, a pyramid like that would never be constructed!" That's not the point here. Even if you're rounding to the nearest hundredth, that's not very hard to do; what's important is the process to get to the answer, not so much the answer itself.
Sorry jfan, I am with Spongebob on this one.
The question is about the cost of dinners. It is not a theoretical question.
The answer MUST be rounded off to give a dollars and cents answer.
Exactly how it is rounded may be open to interpretation but it must be rounded. The waitress cannot charge a part of a cent.
Also, I have not looked at your answer thoroughly, but it seems to me that you have allowed the calculator to round anyway.
Your answer does not look exact to me.
Rounding to 2 decimal would make a lot more sense.,
Your cut a penny joke is funny, SpongeBob.
You are also correct that the result should be calculated to the nearest cent. All the data is presented to the nearest cent; using more significant digits is superfluous. If the question indicated this was to be used as a statistic for a chain of a thousand plus restaurants, then the third decimal place would be significant in that collective.
Jfans analogy comparing the use of significant digits to that of a hypothetical question where the construct could not or is not likely to exist in the real world is non sequitur. Hypothetical questions are common in mathematics and physics. For example, physics questions will often say to ignore air resistance or other frictions that would normally be present in reality. The purpose of this is to quantize the learning process. There are also real environments where such frictions are insignificant and all of these question types have an at least an implied final significant digit count. There usually is not a need to carry significant digit use to extremes. So, how many digits of /pi do we need?
Hypothetical future conversation... sometime after SpongeBob reattaches his corpus spongiosum appendage handed to him by jfran.
Jfan17: The problem is you are a generalist and I am a perfectionist.