SOLUTION: If the same number is added to both the numerator and the denominator of the amount of butter use in the following recipe for toffee the result is the amount of brown sugar to be

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If the same number is added to both the numerator and the denominator of the amount of butter use in the following recipe for toffee the result is the amount of brown sugar to be      Log On


   

Question 1117619: If the same number is added to both the numerator and the denominator of the amount of butter use in the following recipe for toffee the result is the amount of brown sugar to be find a number
2/3 pecans
3/4 cup brown sugar
1/2 package (6-oz size)
1/4 cup butter
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe, add x to numerator and denominator,
%281%2Bx%29%2F%284%2Bx%29=3%2F4, to get the amount of brown sugar, cups




-----------------------this, misunderstanding of the description-----------
The butter:
%281%2Bx%29%2F%284%2Bx%29


The amount of brown sugar needed would be
%28%281%2Bx%29%2F%284%2Bx%29%29%28%283%29%2F%281%29%29

3%28x%2B1%29%2F%28x%2B4%29 cups

Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


I have no idea what the other tutor's response means. Either I or that tutor has misread the problem....

We want a number x for which
%281%2Bx%29%2F%284%2Bx%29+=+3%2F4

A solution using algebra is a good exercise in the methods of algebra:
4%281%2Bx%29+=+3%284%2Bx%29
4x%2B4+=+3x%2B12
x+=+8

But probably the fastest way to an answer, if an algebraic solution is not necessary, is to look at fractions equivalent to 3/4 and find one which is in the form %281%2Bx%29%2F%284%2Bx%29

6%2F8+=+%281%2B5%29%2F%284%2B4%29 no...
9%2F12+=+%281%2B8%29%2F%284%2B8%29 YES!!

Solving problems informally using logical reasoning is always good mental exercise!