Acustomer is owed $30.00. how many different combinations of bills, using only five, ten, and twenty dollars bills are possible to give his or her change?

1.  6 fives.

2.  1 ten and 4 fives.

3.  2 tens and 2 fives.

4.  3 tens.

5.  1 twenty and 2 fives.

6.  1 twenty and 1 ten.

Step-by-step explanation:

Given : A customer is owed $30.00.

To find : How many different combinations of bills,using only five, ten, and twenty dollars bills are possible to give his or her change?

Solution :

We have to split $30 in terms of only five, ten, and twenty dollars.

1) In terms of only five we required 6 fives as

So, 6 fives.

2) In terms of only ten and five,

a) We required 1 ten and 4 fives as

So, 1 ten and 4 fives.

b) We required 2 tens and 2 fives as

So, 2 tens and 2 fives

3) In terms of only tens we require 3 tens as

So, 3 tens.

4)  In terms of only twenty and five, we required 1 twenty and 2 fives as

So, 1 twenty and 2 fives.

5)  In terms of only twenty and ten, we required 1 twenty and 1 ten as

So, 1 twenty and 1 ten.

Therefore, There are 6 different combinations.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4