SOLUTION: Suppose you spend $23 and you pay with a $50 bill. The cashier gives your change in bills. List all the different ways you can receive your correct change if you will not take more

Question 947502: Suppose you spend $23 and you pay with a $50 bill. The cashier gives your change in bills. List all the different ways you can receive your correct change if you will not take more than 10 bills and the cashier only has 1s, 5s, and 10s. Show your work.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
u, f, t, how many of the "units", fives, and tens.

No more than ten bills, means . Might start first with the equality of this.

Amount of change will be $27, so .

The best way to find all the combinations is to form tree-diagrams, not to try any simultaneous equations. Start with the most efficient combination first, and then work from there to make the less efficient combinations. The most efficient bill combination is t=2, f=1, u=2.
Next, split the f into five of the units, so have t=2, f=0, u=2+5=7.

Continue looking for more ways to split more of the bills...

I did not finish this, but only described how to find the combinations.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Suppose you spend $23 and you pay with a $50 bill. The cashier gives your change in bills. List all the different ways you can receive your correct change if you will not take more than 10 bills and the cashier only has 1s, 5s, and 10s. Show your work.

There are ways
You can do the check!!
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