Question 348015: Kelly claims, "It is possible for 46 pennies and nickels to have a total value of a dollar." Is she right or wrong? Give a convincing argument to justify your answer.
Found 2 solutions by Alan3354, texttutoring:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Start with 46 pennies, = 46 cents.
For each penny replaced by a nickel, the total increases by 4 cents.
To increase the total to $1, the increase would be 54 cents.
54/4 is not an integer, so it's not possible.
Answer by texttutoring(324)  (Show Source):
You can put this solution on YOUR website! She is wrong. You can prove it by using some trial and error examples or by using two formulas.
With trial and error:
15 nickels = $0.75
That would leave 25 pennies to equal $1.00. But that would only add up to 40 coins.
14 nickels = $0.70
That would leave 30 pennies to equal $1.00. But that would only add up to 44 coins.
13 nickels = $0.65
That would leave 35 pennies to equal $1.00. But that would add up to 48 coins, which is too many.
Using formulas, it would look like this:
Let p= number of pennies
Let n = number of nickels
Equation 1: n+p = 46
Equation 2: 0.05n + 0.01p = 1.00
Using substitution method or elimination method, you will find that p = 32.5. Of course, you can't cut a penny in half, so this shows that n+p cannot equal 46 coins.
If you need clarification on anything, or want more details about how to solve those two equations, please let me know.
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