SOLUTION: Betty baked some cheese buns and butter buns. After she sold 1/3 of the cheese buns and 2/5 of the butter buns, she had 50% as many butter buns as cheese buns left. What fraction o

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Question 1203331: Betty baked some cheese buns and butter buns. After she sold 1/3 of the cheese buns and 2/5 of the butter buns, she had 50% as many butter buns as cheese buns left. What fraction of the buns baked was butter buns?
Found 3 solutions by greenestamps, MathTherapy, josgarithmetic:
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


I thought of several different ways to attack this problem and couldn't decide easily which one would be easier, so I tried different ones.

That in itself is a good lesson in problem solving, whether it is a math problem or a problem in real life. Always be open to trying different ways of doing things. If we didn't do that, we would all still be living in caves.

Method 1...

let b = # of butter buns
let c = # of cheese buns

The number we are to find is the fraction of the buns that are butter buns. That fraction is b/(b+c).

She sold 1/3 of the cheese buns, so the number she had left was (2/3)c.

She sold 2/5 of the butter buns, so the number she had left was (3/5)b.

The number of butter buns she had left was half the number of cheese buns; i.e., the number of cheese buns she had left was twice the number of butter buns.






ANSWER: 5/14

Method 2...

let x = # of butter buns she had left
then 2x= # of cheese buns she had left

She sold 1/3 of the cheese buns, so she was left with 2/3 of them. She was left with 2x cheese buns, so the number she started with was (3/2)(2x) = 3x.

She sold 2/5 of the butter buns, so she was left with 3/5 of them. She was left with x butter buns, so the number she started with was (5/3)x.

She started with (5/3)x butter buns and 3x cheese buns. The fraction of buns that were butter buns was



ANSWER: 5/14

Method 3...

let x = fraction of the buns that were butter buns
then 1-x = fraction that were cheese buns

She was left with (3/5)x butter buns and (2/3)(1-x) cheese buns; and the number of cheese buns left was twice the number of butter buns left:







ANSWER: 5/14

Having solved the problem three different ways, I see tricky parts in each of the methods, so I don't have a strong preference for any one of them....

Perhaps another tutor will present a different method for solving the problem that is easier than any of the above.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Betty baked some cheese buns and butter buns. After she sold 1/3 of the cheese buns and 2/5 of the butter buns, she had 50% as many butter buns as cheese buns left. What fraction of the buns baked was butter buns?

Let number of cheese, and butter buns baked, be C and B, respectively
As she sold  of cheese buns,  remained
As she sold  of butter buns,  remained
Since 50% as many butter as cheese remained, we get: 
                                                      5C = 9B ---- Cross-multiplying
                      Number of cheese buns baked, or 

Number of buns baked: C + B = 1.8B + B = 2.8B

Number of butter buns baked: B
Fraction of buns baked that were butter:

Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
BUNS          SOLD      REMAINING
  q            q/3        2q/3
  m           2m/5        3m/5

------------------------------------------------------------
...she had 50% as many butter buns as cheese buns left.
------------------------------------------------------------


-





ORIGINALLY BAKED
of the cheese buns
of the butter buns

---------------------------------------------------
What fraction of the buns baked was butter buns?
---------------------------------------------------





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