Stella has 3 quarters and 4 dimes. How many different
amounts can she form with these 7 coins, using at
least on coin each time?

answer is 19...kaplan's explanation makes me want to kick someone in the face, so i wanna try my luck here...

bump?

Start off with just combos of one of each coin....

1Q
2Q
3Q

1D
2D
3D
4D

7 Combos

Then a combo of 1Q with 1, 2, 3, and 4D respectively. (4 Combos)

Do that for 2Q and 3Q as well.

19 total

is there any other way than to think and write out all the possibilities? under test stress and time pressures i can easily forget one or double count so is there any way other than to list it all out?

is there any other way than to think and write out all the possibilities? under test stress and time pressures i can easily forget one or double count so is there any way other than to list it all out?

I bet someone on here (smarter than I) can come up with some formula for this, but from my limited DAT studying so far, I've found that writing it out works the best for me for this kind of problem.

Well no amount of either coin type can equal any amount made by the other type of coin (had there been 5 dimes you would either count 5 dimes or 2 quarters but not both because they equal the same amount).

So 3 quarters can be used 4 ways: 0Q, 1Q, 2Q, or 3Q.
Similarly, 4 dimes can be used 5 ways: 0D, 1D, 2D, 3D, or 4D.

So 4x5 = 20. But since we don't want 0Q + 0D, we really only have 19.

is there any other way than to think and write out all the possibilities? under test stress and time pressures i can easily forget one or double count so is there any way other than to list it all out?

3X4 = 12

FOr each amount of quarters (1Q, 2Q, 3Q) you can have 4 amounts of dimes (1D, 2D, 3D, 4D). That is 12 combos.

Plus you have 7 amounts of just one coin.

12+7 = 19.

It is a lot like a branch diagram in genetics if you want to think of it that way.

oh okay this sounds good too. I like the multiplication versus remembering all the combos. I'm just nervous under pressure and time i'd miss a combo so multiplying them out seems a little safer

thank you!:)