homework help?

Question

Jayne has 3 quarters,2 dimes,a nickel,and 2 pennies in her pocket. How many different amounts of money can she make using some or all of these coins?

Answer 1

12 different amounts.

Use the fundamental counting principle to get your answer.
3 x 2 x 1 x 2 = 12

Hope I helped. Good luck! :)

Answer 2

you could use what roxy said, 3*2*1*2 if your problem said "how many different combinations can you make with the numbers 3, 2, 1, and 2", but you can't do that here, because you have to consider all possible amounts, including those when 0 quarters are used, or 0 dimes ...

there is probably a formula for this, but I don't know it. What you have to do is make a "t chart" of all possible combinations

you can use either 0, 1, 2, or 3 quarters.

for each one of those choices you can use either 0, 1, or 2 dimes.

and then for each one of those choices you can use either 0 or 1 nickels

and finally for each one of those choices you can use either 0,1,or 2 pennies

when you draw out this chart, you start with the 0, and you branch out to 0, 1, or 2 dimes
from each one of those you branch out to 0 or 1 nickels, and from there you branch out to 0,1, or 2 pennies.

it will start out like this (ignore the ...)
....0
../
0 -1
..\
....2

then you repeat this process for 1 quarter, for 2 quarters, and for 3 quarters

what this does is shows every possible "path", or combination of quarters, dimes, nickels, and pennies.
after this is drawn, you just have to count the number of paths.
on the first branch (starting with 0), there are 18 paths
and since there are four of these that means there are 72 total paths

but your question asks how many DIFFERNT amounts can be made, so now you have to see if all of these are different or not.

using your chart, figure out each of the amounts, and you will see that 9 of them are repeated

what causes them to be repeated is the fact that 1 quarter is the same as 2 dimes and 1 nickel, so having 0 quarters, 2 dimes, 1 nickel, and 0 pennies is the same as having 1 quarter, 0 dimes, 0 nickels, and 0 pennies

anyway, there are 9 of these, and you will see the pattern on your chart

since 9 out of the 72 amounts were repeated, that means 63 different amounts are possible