Jason S. answered • 10/17/13
Tutor
4.9
(116)
My goal is the success of my students. Knowledge-Patience-Honesty
(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.
(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.
Jason S.
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
Report
10/17/13
Jason 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
Report
10/17/13
Andrea T.
thank you. why do i have to multiply by 4/3 on both sides?
Report
10/17/13
Jason S.
You want to divide by 3/4 to isolate the variable l, which is the same as multiplying by its reciprocal, 4/3.
Report
10/17/13
Andrea T.
10/17/13