The total amount of change, in cents, that was found is determined as 96 cents.
<h3>Total amount of change</h3>
The total amount of change is calculated as follows;
let the total = T
there was at least one coin of each type
T = p + n + d + q
more than half of the coins were pennies
<h3>Value of the coins</h3>
- pennies = $0.01
- nickels = $0.05
- dimes = $0.1
- quarters = $0.25
more than half = pennies
next, we have; nickels + dimes + quarters
<h3>number of dimes</h3>
y(dimes) = $0.25
y(0.1) = 0.25
y = 0.25/0.1
y = 2.5 ≅ 3
dimes = 3 coins
<h3>number of nickels</h3>
since dimes = 3 coins, number of nickels is now calculated as;
x(0.05) = 3(0.1)
x = (0.3)/(0.05)
x = 6 coins
nickels = 6 coins
<h3>Total coins</h3>
Total coins = nickels + dimes + quarters + pennies
- pennies must greater than 6 coins, since we can't have fewer coins.
Total coins = nickels + dimes + quarters + pennies
let pennies = 7
Total coins = 6 + 3 + 1 + 7
Total coins = 17
half of 17 = 8.5
7 is less than half (8.5), number of pennies cannot be 7, since more than half of the coins are pennies.
let pennies = 11
Total coins = 6 + 3 + 1 + 11
Total coins = 21
half = 10.5
- 11 is more than half (10.5)
more than half = number of pennies = 11
<h3>Total amount in cents</h3>
11($0.01) + 6($0.05) + 3($0.1) + 1($0.25) = $0.96 = 96 cents
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