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2 years ago

Can someone help me with this problem I really don’t know how to work it out and I’m getting frustrated please help..

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

7 0

Answer:

1 cake and 6 pies

Step-by-step explanation:

Let c represent the number of cakes Alice and George can make. Likewise, let p represent the number of pies.

Then the amount of flour they need (in cups) is ...

3c + 2p . . . . cups of flour needed

And the amount of sugar needed is ...

2c + 1.5p . . . cups of sugar needed

They want to use all 15 cups of flour they have, and all 11 cups of sugar, so the amounts above need to match the amounts on hand:

3c + 2p = 15

2c + 1.5p = 11

We can solve these equations various ways. One of my favorite is to use a graphing calculator. (See attached) It tells us that Alice and George can make 1 cake and 6 pies with the flour and sugar they have.

_____

If you want to solve these equations algebraically, there are several methods for that, too. Here, we can multiply the first one by 2/3 and subtract the result from the second one:

(2c +1.5p) -(2/3)(3c +2p) = (11) -(2/3)(15)

2c +3/2p -2c -4/3p = 11 -10 . . . . . eliminate parentheses

1/6p = 1 . . . . . . . . . . . . . . . . . . . . . .collect terms

p = 6 . . . . . . . . . . . . . . . . . . . . . . . . multiply by 6

Substituting into the first equation gives ...

3c +2·6 = 15 . . . substitute 6 for p

3c = 3 . . . . . . . . subtract 12

c = 1 . . . . . . . . . . divide by 3

These values tell us Alice and George can make 1 cake and 6 pies with the flour and sugar they have.

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Given:

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To find:

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Solution:

Distance formula:

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Using distance formula, we get

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Both diagonals are equal.

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It means that maximum of 2 members can have the same station. Cases for this situation are as follows:

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