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# Difficult Problem of Proportions

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Ice-cream-o-Rama is eager to advertise how many flavors it has. But it really only has three basic flavors: chocolate, vanilla, and strawberry. However, they can make "new" flavors by taking four scoops of ice cream of those basic flavors and blending them together. Different proportions of the basic flavors give different new flavors. How many total flavors can Ice-cream-o-Rama now advertise?

This is really difficult, can I get help?

Oct 23, 2017

#1
+98125
+2

We have to take at least two scoops of one flavor if we use 4 scoops

I'm also assuming that we don't necessarily have to use all the flavors at once, but we must use at least two of the flavors

Here's the way I would do this.......but....maybe not the fastest

Flavors     Vanilla      Chocolate   Strawberry

Scoops      2                 1                 1

1                 2                 1

1                 1                 2

1                 3                 0

2                 2                 0

3                 1                 0

1                 0                 3

2                 0                 2

3                 0                 1

0                 1                 3

0                 2                 2

0                 3                 1

If we have to use all 3 flavors......there are 3 new flavors......using my assumption adds 9 more

Oct 23, 2017
#2
+445
+2

You can have plain flavors without mixing them together so that gives 3 plus all the mixtures.

Mr.Owl  Oct 23, 2017
#3
+98125
+2

We have 12 in total if we have to use at least two of the flavors......if we can have 4 scoops of only one flavor....then just add 3 to this giving 15 in all

Oct 23, 2017