Question 1170013: fourteen articles are bought. Some cost $2.00 each and the remainder cost $2.25 each.If the total amount spend is $30, how many of each article are bought
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
(1) Using formal algebra....
x = # articles at $2 each
(14-x) = # articles at $2.25 each
Solve using basic algebra.
You should certainly know how to set up and solve the problem like that, or in another similar way, using formal algebra.
If a formal algebraic solution is not required (for example, in a timed math competition where getting an answer as fast as possible is desired), there are many other ways to solve the problem.
(2) Informally, using logical reasoning and some simple arithmetic....
All 14 articles at $2.00 each would be $28.00, which is $2.00 short of the actual total.
Each of the articles selling for $2.25 costs $0.25 more than one selling for $2.00.
The number of articles selling at $2.25 each, in order to make up the additional $2.00, is $2.00 divided by $0.25, which is 8.
ANSWER: 8 articles at $2.25 each and 14-8=6 articles at $2.00 each.
CHECK: 8(2.25) + 6(2.00 = 18+12 = 30
(3) And yet another solution using logical reasoning....
The total cost is an even whole dollar amount; and the total cost of any number of $2.00 items will be an even whole dollar amount.
So the total cost of the items at $2.25 each must be an even whole dollar amount.
The only number of items (less than 14) at $2.25 each for which the total is an even whole number of dollars is 8: 8($2.25) = $18.
So there must be 8 items at $2.25 each and 14-8=6 items at $2 each.
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