Question 1029360: Calculators cost $24 each and markers cost $6 each. How many combinations of calculators and markers can be purchased for between $72 and $120, inclusive?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
Calculators cost $24 each and markers cost $6 each. How many combinations of calculators and markers can be purchased for between $72 and $120, inclusive?
Solution:
We note that it "happens" that $72 can buy 3 calculators, and $120 can buy 5 calculators, both exactly.
Also, each calculator at $24 is worth 4 markers at $6 each.
We'll start by figuring out how many combinations of calculators (C) and markers (M) can be bought for $72.
$72
C M
3 0
2 4
1 8
0 12
Total 4 combinations
For $78, we can buy
C M
3 1
2 5
1 9
0 13
4 combinations and 4 each for $84 and $90 for a total of 12 combinations
So between $72 and $90 there are 4*4=16 combinations.
Similarly, between $96 and $114 there are 4*5= 20 combinations
and $120 has 6 combinations.
The grand total is therefore 16+20+6=42 combinations.
Note: the above calculations are for the case where exact purchases are assumed, i.e. disregarding cases of having money left over. This is because the combination of calculators and markers does not change when we have money left over, for example, $73 will still buy the same combination of markers and calculators as $72 would.
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