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Answer:
$5.83
Step-by-step explanation:
The total amount of money is the sum of the values of the various denomination coins.
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Let p, n, d, q represent the numbers of pennies, nickels, dimes, and quarters, respectively.
p + n + d + q = 50 . . . . . . there are 50 coins in all
16% × 50 = p . . . . . . . . . . 16% are pennies
34% × 50 = d . . . . . . . . . . 34% are dimes
n = p +3 . . . . . . . . . . . . . . there are 3 more nickels than dimes
The total value is ...
v = 0.01p +0.05n +0.10d + 0.25q
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The numbers of pennies and dimes are found easily:
0.16 × 50 = p = 8
0.34 × 50 = d = 17
Then the number of nickels can be found:
n = p +3 = 8 +3 = 11
Finally, the number of quarters is found from the total number of coins:
p + n + d + q = 50
8 + 11 + 17 + q = 50 . . . substitute known values
q = 14 . . . . . . . . . . . . . subtract 36 from both sides
The total value is then ...
v = 0.01(8) +0.05(11) +0.10(17) +0.25(14) = 0.08 +0.55 +1.70 +3.50
v = 5.83
The bag contains $5.83.