SOLUTION: Frank bought 2 shirts and 1 pair of dress pants for a total of $55. If he had bought 1 shirt and 2 pairs of dress pants, he would have paid $68. What was the price of each shirt an

Question 1152425: Frank bought 2 shirts and 1 pair of dress pants for a total of $55. If he had bought 1 shirt and 2 pairs of dress pants, he would have paid $68. What was the price of each shirt and each pair of dress pants?
Found 2 solutions by josmiceli, greenestamps:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the price of a shirt
Let = the price of pants
--------------------------------------
(1)
(2)
----------------------------
(2)
Plug this result back into (1)
(1)
(1)
(1)
(1)
and
(1)
(1)
(1)
----------------------
$14 = the price of a shirt
$27 = the price of pants
--------------------------------
check:
(1)
(1)
you can do (1) and (2)

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Translating the given information directly into equations gives us

While solving that pair of equations using substitution, as the other tutor did, is valid, there are other ways that are far less work.

The solution with formal algebra using substitution is hard to interpret in everyday language; there are at least a couple of ways to solve the pair of equations using formal algebra for which it is easy to see how common sense makes the solution processes easy to understand.

Here are a couple of solutions that use algebra that is easily described in everyday language.

(1) One standard method for solving pairs of linear equations -- and the most straightforward when the information is given in this way -- is elimination: multiply one or both equations by some constant so that you can use the two resulting equations to eliminate one variable by either adding or subtracting the two equations.

In common sense language, suppose that, instead of buying 1 shirt and 2 pairs of pants for $68, he bought 2 shirts and 4 pairs of pants. That would cost him $136. Algebraically, "multiply the second equation by 2":

-->

Now compare the two purchases (subtract the first equation from this new equation):

and --> --> y=27

In everyday language, the difference between the two purchases is now 3 extra pairs of pants, for an extra $81; that means each pair of pants costs $81/3 = $27.

Then use that fact with any of the purchases to determine the cost of each shirt.

(2) And here is a method that uses an unusual algebraic approach but is very understandable with common sense.

Between the two purchases described in the problem, the difference is one more pair of pants and one less shirt, for an increase of $13 in the total cost. (Algebraically, to find the difference between the two purchases, subtract the first equation from the second):

and -->

So let's make a third purchase where we again add one pair of pants and subtract one shirt. That gives us three pairs of pants and no shirts, for a cost of $68+$13 = $81.

So again we find the cost of each pair of pants to be $81/3 = $27.
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