9514 1404 393
Answer:
$12 for each shirt
Step-by-step explanation:
If we let 's' and 't' represent the costs of a shirt and tie, respectively, then we can write the general form equations ...
6s +3t -79.50 = 0
3s +2t -41.00 = 0
The solution for s can be found using the "cross multiplication" technique.
Differences of products can be formed:
d1 = (6)(2) -(3)(3) = 3
d2 = (3)(-41) -(2)(-79.50) = 36
Then we have ...
1/d1 = s/d2 ⇒ s = d2/d1 = 36/3 = 12
The cost of each shirt is $12.00.
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2 ties cost 41-36 = 5, so each one is $2.50.
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<em>Additional comment</em>
The use of simple elimination on this set of equations would eliminate the s-variable, so would mean additional work to find s after finding t. The t-variable could be eliminated by multiplying one equation by one coefficient, and the other by a different coefficient. As long as we're doing that amount of work, we may as well do just enough cross-multiplication to get the one answer we need. This is where the "cross-multiplication" method of solution comes in handy.
This method solves the general-form equations ...
- ax +by +c = 0
- dx +ey +g = 0
by considering the two rows of coefficients:
Then differences of cross-products are formed in adjacent columns:
d1 = ae -db
d2 = bg -ec
d3 = cd -ga
The solutions are ...
1/d1 = x/d2 = y/d3 ⇒ x = d2/d1, y = d3/d1
