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Orange and Grape Sodas

```Date: 08/24/2002 at 10:17:40
From: Dustin
Subject: Guess and check problem

Douglas bought a total of 50 cans of orange and grape sodas. He bought
12 more cans of grape than orange. How many of each did he buy?

I have subtracted, added, and multiplied, and still can't get the

Dustin
```

```
Date: 08/24/2002 at 10:58:21
From: Doctor Sarah
Subject: Re: Guess and check problem

Hi Dustin - thanks for writing to Dr. Math.

Are you allowed to use a little algebra?

You could let the cans of orange soda equal x. Then the cans of grape
soda will be x+12, and the total will be 50:

x + x + 12 = 50

Collect like terms (the x's):

2x + 12 = 50

Subtract 12 from both sides of the equation:

2x = 38

Divide both sides of the equation by 2:

x = 19  (number of cans of orange soda)

x + 12 = 31  (number of cans of grape soda)

Does 19 + 31 equal 50?

- Doctor Sarah, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 08/25/2002 at 15:33:46
From: Doctor Greenie
Subject: Re: Guess and check problem

Hi, Dustin -

Her response was perfectly correct and appropriate - if you are
allowed to use algebra. However, it appears likely to me that, if you
are really 11 years old, then you aren't expected to use algebra in
the solution of the problem. Here is another approach to the
problem which you can use to get the answer without using algebra:

The problem says Douglas bought 12 more cans of grape soda than of
orange, and that he bought a total of 50 cans of soda. Suppose, for
the moment, we "take away" those 12 extra cans of grape soda from the
problem - what do we have then?  Now, without those 12 "extra" cans
of grape soda, he has bought the same number of cans of orange and
grape sodas, and he has bought a total of 38 cans (50 - 12) of soda.
That means he has bought 19 (half of 38) cans of each type of soda.
Now we add those 12 extra cans of grape soda back into the problem
and find that he bought 19 cans of orange soda and 31 cans (19 + 12)
of grape soda.

If you haven't yet started to learn any algebra, it might be
interesting to compare my response to the one provided earlier by
Doctor Sarah. You might see that the path to the solution using the
formal algebra of her approach and the logical reasoning of my
approach are in fact virtually identical - hers just uses the formal
responses, you might be able to see how algebra is used to solve
problems like this in a formal manner.

- Doctor Greenie, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 08/26/2002 at 15:13:34
From: Dustin
Subject: Thank you (Guess and check problem)

Dr. Greenie,

Thank you so much for your answer on the sodas. I really appreciate
it. This makes more sense than the other way. I don't think I should
be having algebra either in the 6th grade. Maybe this will help me.

Thanks again,
Dustin
```
Associated Topics:
Elementary Word Problems
Middle School Algebra
Middle School Word Problems

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