SOLUTION: A purse contains 30 coins, all either quarters or dimes. The total value of the coins is greater than $5.20. At least how many of the coins are quarters? At most how many are dimes

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Question 75171: A purse contains 30 coins, all either quarters or dimes. The total value of the coins is greater than $5.20. At least how many of the coins are quarters? At most how many are dimes?
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=number of quarters
Then 30-x=number of dimes
(Lets deal in pennies to keep down confusion and simplify the problem)
Now we are told that:
25x+10(30-x)>520 get rid of parens
25x+300-10x>520 subtract 300 from both sides
25x-10x+300-300>520-300 collect like terms
15x>220 divide both sides by 15
x>14.667 This answer tells us that we have to round up to the nearest whole number because the number of quarters cannot be less than 14.667. So:
x>=15 which means there's at least 15 quarters
If there's at least 15 quarters, then there's at most 15 dimes.
x>=15 multiply both sides by -1 (must reverse inequality sign)
-x<=-15 add 30 to both sides
30-x<=30-15 so
30-x<=15-------------------which means there's at least 15 dimes
CK
15*10+15*25>520
150+375>520
525>520
now lets try 14 quarters and 16 dimes----this should not work
14*25+16*10>520
350+160>520
510 is not greater than 520

Hope this helps----ptaylor