Case 1: If we don't use any quarters, then we must make the whole
48 cents with dimes, nickels and pennies.
A. If we use 0 dimes we can use 0 up to 9 nickels and the rest pennies.
That's 10 ways.
B. If we use 1 dime we can use 0 up to 7 nickels and the rest pennies.
That's 8 ways.
C. If we use 2 dimes we can use 0 up to 5 nickels and the rest pennies.
That's 6 ways.
D. If we use 3 dimes we can use 0 up to 3 nickels and the rest pennies.
That's 4 ways.
D. If we use 4 dimes we can use 0 or 1 nickel and the rest pennies.
That's 2 ways.
So with no quarters there are 10+8+6+4+2 or 30 ways
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Case 2: If we use 1 quarter, we have to make the remaining 23 cents with
dimes, nickels, and pennies
A. If we use 0 dimes we can use 0 up to 4 nickels and the rest pennies.
That's 5 ways.
B. If we use 1 dime we can use 0 up to 2 nickels and the rest pennies.
That's 3 ways.
C. If we use 2 dimes we can only use 3 pennies.
That's 1 way.
So with 1 quarter there are 5+3+1 or 9 ways to make the remaining 23 cents.
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30 ways using 0 quarters
9 ways using 1 quarter
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total: 39 ways to have 48 cents in coin.
Edwin
