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 beef and chicken, find the total weight of chicken the butcher has.

121 pounds of chicken

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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Cramer's Rule

For equations ...

Cramer's rule tells you the solutions are ...

... ∆ = bd-ae

... x = (bf -ec)/∆

... y = (cd -fa)/∆

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Comment on Cramer's Rule

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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