Question 1185563
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The fastest way to find the answer is by logical reasoning with some simple mental arithmetic.<br>
With a total value of #3.57, the number of pennies must be one of these numbers:<br>
2, 7, 12, 17, ...<br>
So try one of those and see if it works; then adjust if needed.<br>
17 pennies would mean 60-17=43 dimes; $0.17+$4.30 = $4.47.  Too much.<br>
Maybe next try 37 pennies and 23 dimes: $2.30+$0.37 = $2.67.  Too little.<br>
Looking at those results and doing some easy calculations shows the correct total is exactly halfway between our two guesses.<br>
So try 27 pennies and 33 dimes. $3.30+$0.27 = $3.57.  Just right.<br>
ANSWER: 33 dimes and 27 pennies<br>
And here is another path that can teach you a good problem solving strategy when you are using guess-and-check.<br>
After finding that 17 pennies and 43 dimes was $4.47, which is $0.90 too much, you can logically reason that exchanging a dime for a penny reduces the total value by $0.09.  So to reduce the total $4.47 by $0.90 to get the correct total of $3.57, you need to exchange 10 dimes for pennies.<br>
So the correct combination is 43-10=33 dimes and 17+10=27 pennies.<br>
But probably a formal algebraic solution is wanted....<br>
x = # of dimes
60-x = # of pennies<br>
The total value is $3.57 = 357 cents<br>
10x+1(60-x)=357
10x+60-x=357
9x=297
x=33<br>
ANSWER: x=33 dimes, 60-x=27 pennies<br>