Question 998159
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Solve the problem using logical reasoning and simple mental arithmetic.<br>
(1) A total of 127 cents with 11 coins means there must be 2 pennies.<br>
(2) Then, since the number of quarters is twice the number of pennies, the number of quarters is 4.
(3) That makes 6 coins with a total value of $1.02.
(4) The remaining 25 cents is made up of 5 nickels.<br>
ANSWER: 2 pennies, 4 quarters, 5 nickels.<br>
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If you need a solution using formal algebra, set the problem up using a single variable -- not three different variables for the numbers of pennies, nickels, and quarters.<br>
Let x = # of pennies
Then 2x = # of quarters
Then 11-3x = # of nickels.<br>
The total value of the coins is 127 cents.<br>
{{{1(x)+25(2x)+5(11-3x) = 127}}}
{{{x+50x+55-15x = 127}}}
{{{36x = 72}}}
{{{x = 2}}}<br>
ANSWER:
# of pennies: x = 2
# of quarters: 2x = 4
# of nickels: 11-3x = 5<br>