SOLUTION: In Stephen’s piggy bank there are as many nickels as pennies three more dimes the. Nickels and five fewer quarters than pennies. If he has 3.97 in his bank how many of each kind

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Question 1208876: In Stephen’s piggy bank there are as many nickels as pennies three more dimes the. Nickels and five fewer quarters than pennies. If he has 3.97 in his bank how many of each kind of coin does he have
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Written more clearly, As many nickels as pennies, three more dimes than nickels, and five fewer quarters than pennies. He has $3.97. 


COIN        QUANTITY       AMOUNT
penny          x            0.01x
nickel         x            0.05x
dime           x+3          0.1(x+3)
quarter        x-5          0.25(x-5)

TOTAL                       3.97

0.06x%2B0.1%28x%2B3%29%2B0.25%28x-5%29=3.97

0.06x%2B0.3%2B9.1x-0.25%2A5%2B0.25x=3.97
%280.06%2B0.1%2B0.25%29x%2B0.3-0.25%2A5=3.97
0.41x=3.97-0.3%2B1.25
0.41x=4.92
x=4.92%2F0.41
highlight%28x=12%29, and from this you can find the others.

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


The formal algebraic solution from the other tutor is fine. Note, however, that most students at any level will find it easier to work the problem in cents instead of dollars so that all the calculations are in whole numbers instead of decimals.

But you can get good problem-solving practice by solving a relatively simple problem like this using logical reasoning and simple arithmetic. Here are two such solutions.

(1) Changing the numbers of each kind of coin

Take away the three "extra" dimes so that the numbers of pennies, nickels, and dimes are all the same; that makes the total value of the coins $3.97 - $0.30 = $3.67.

Similarly, add five more quarters so that the numbers of all denominations of coins are the same. The new total value is $3.67 + $1.25 = $4.92. Let's change that to 492 cents to continue with the problem.

There are now equal numbers of pennies, nickels, dimes, and quarters. The value of one of each of those coins is 1+5+10+25 = 41 cents.

Divide the new total of 492 cents by 41 cents to find that there are 12 of each coin.

ANSWERS:
pennies: 12
nickels: 12
dimes (3 more than that): 15
quarters (5 fewer than that): 7

CHECK: 12(1) + 12(5) + 15(10) + 7(25) = 12+60+150+175 = 397 cents = $3.97

(2) Using logical reasoning, along with the given total value of $3.97 and the fact that the total value of the nickels, dimes, and quarters is a multiple of 5 cents, to solve the problem using "smart" trial and error.

With a total value of 397 cents, the number of pennies can only be 2, or 7, or 12, or 17, or....

There can't be only 2 pennies, because the number of quarters is 5 less than the number of pennies.

If there were 7 pennies, then the number of quarters would be only 7-5 = 2, and you aren't going to get a total of 397 cents with just 2 quarters.

Trying 12 pennies next, we find that gives us the correct total value of 397 cents.

From there the solution is the same as above.