1/3 the weight of beef and 1/4 the weight of chx make up 54 3/4 pounds of meat he has. if he has a total of 194 1/2 pounds of be
ef and chicken, find the total weight of chicken the butcher has.
1 answer:
<h3>Answer:</h3>
121 pounds of chicken
<h3>Explanation:</h3>Let x and y represent pounds of beef and chicken, respectively. Then the problem statement gives rise to two equations:
... (1/3)x + (1/4)y = 54 3/4
... x + y = 194 1/2
We can use Cramer's Rule to solve for y.
... y = ((54 3/4)·(1) -(194 1/2)·(1/3))/((1/4)·(1) -(1)·(1/3))
... y = (-121/12)/(-1/12)
... y = 121
The butcher has 121 pounds of chicken.
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<em>Cramer's Rule</em>
For equations ...
- ax +by = c
- dx +ey = f
Cramer's rule tells you the solutions are ...
... ∆ = bd-ae
... x = (bf -ec)/∆
... y = (cd -fa)/∆
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<em>Comment on Cramer's Rule</em>
If you're only interested in one of the variables, quite often this technique is faster than other processes that might be used to find the value. If you examine the rule's equations closely and look at the pattern of coeffcients used, you may find it relatively easy to remember.
The actual "Cramer's Rule" uses the negative of the numerator and denominator expressions shown here. It is based on column replacement in the coefficient matrix. This form is promoted by practitioners of Vedic math because it is relatively easy to remember the pattern and most of the time the math can be done in your head (though you might find it difficult with these mixed numbers).
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Here's a picky pickypoint to think about concerning the "cost". I'm not quite sure what to do about this:
The initial, one-time $55 is a "deposit". If she doesn't smash the bike or steal it, she gets the $55 back when she returns the bike.
So if she eventually gets the $55 back, <u><em>is it a cost</em></u> ? ? I don't know how to think about it.
She does need to <em>give</em> them the $55 at the beginning, just to take the bike out. So she has to have it with her and give it to them temporarily, even though she'll get it back, and she'll still have it when she returns home.
So here's the story:
-- While she HAS the bike, the graph correctly shows all the money she needs, in order to get the bike, and keep it for however long she keeps it.
-- Finally, at the end of the week, after she returns the bike and gets her $55 back, the line and everything on the graph will shift down by $55. The line will start at zero, and the little red ordered pairs will also shift straight down and still be on the line.
To put it one more way:
-- While Jen has the bike, the y-intercept of the graph is $55.
-- After she returns the bike in good condition, the y-intercept is zero.
