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Fractioon word problem

Marilyn's recipe for lemondade calls for 3/4 cup of sugar for ever 1/2 cup of lemon juice.  Which of the following equations represents the relationship of cups of lemon juice to cups of sugar in Marilyn's recipe?  Let s = cups of sugar and l = cups of lemon juice
 
a) l=3/8s
b)l = 2/3s
c) l =1 1/2s
d) l=3 2/3s
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2 Answers

(3/4) sugar : (1/2) lemon juice

(3/4)x = (1/2)

Multiple both sides by 4/3

(4/3)(3/4)x = (4/3)(1/2)
x = 2/3

s(2/3) = l

So l = (2/3)s, which means you multiple the number of cups of sugar times 2/3 to get the number of cups of lemon juice.

Let's double-check

l = (2/3)(3/4) (s = # cups of sugar)
l = (6/12) = 1/2

So if s = 3/4 cups of sugar, we need 1/2 cup of lemon juice.
 
b) is correct.

Comments

thanks.  Quick question for you - another tutor answered as well and came up with c as the correct answer.  now i'm confused.
If you are asking for the ratio of cups of sugar to the cups of lemon juice, then Robert is correct.
 
However, the question is asking for the formula for calculating the number of cups of lemon juice BASED on the number of cups of sugar.
 
Since the ratio of s/l = 3 sugar/2 lemon, if you are given sugar, you must put the sugar part of the ratio on bottom, which would flip the 3/2 to 2/3.
 
l = (2/3)s
 
cups of lemon    =   1/2
----------------         -----
cups of sugar          3/4
 
Cross multiply:
 
l(3/4) = s(1/2)
 
Multiply both sides by 4/3...
l (3/4)(4/3) = s (1/2)(4/3)
 
l = s (4/6)
 
l = s (2/3)
 
or 
 
l = (2/3) s
You want to divide by 3/4 to isolate the variable l, which is the same as multiplying by its reciprocal, 4/3.
 
------
My mistake.
l:s = (1/2):(3/4) = 2:3
So, l = (2/3)s

Comments

thanks.  Quick question for you - another tutor answered as well and came up with b as the correct answer.  now i'm confused.
Thanks for the correction Robert.  I had to rethink my answer when I got something different from you.  You do so many on the forum, and do them very well.  
 
I only hope I can contribute as much as you do.