10) Suppose you are an engineer programming the automatic gate for a 45-cent toll. The gate is programmed for exact change only, and will not accept pennies. How many coin combinations must you program the gate to accept?
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Please, give me some minutes to take over your question
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We can solve it by making the list
Coin options: half-dollar coin, quarter, dime, and nickel.
Combinations
1. 0. 25 + 0.15 + 0.05
2. 0. 25 + 0.10 + 0.10
2. 0. 25 + 0.10 + 0.5 * 2
3. 0.25 + 0.5* 4
3. 0.15 * 3
4. 0.15 * 2 + 0.10 + 0.5
5. 0.15 * 2 + 0. 5 * 3
6. 0.15 + 0.10* 3
7. 0.15 + 0.10*2 + 0.5 *2
8. 0.15 + 0.10 + 0.5 *4
9. 0.15 + 0.5 *6
10. 0.10*4 + 0.5
11. 0.10*3 + 0.5*3
12. 0.10*2 + 0.5 *5
13. 0.10 + 0.5 * 7
14. 0.05* 9
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Answer
There are 14 coin combinations to program.