SOLUTION: Dhruv bought some white sugar and some brown sugar. He used an equal amount of white and brown sugar. He had 3/5 of the while sugar and 1/2 of the brown sugar left. What fraction o
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Question 1202921: Dhruv bought some white sugar and some brown sugar. He used an equal amount of white and brown sugar. He had 3/5 of the while sugar and 1/2 of the brown sugar left. What fraction of the sugar which Dhruv bought was used?
(1) 4/7
(2) 4/9
(3) 5/11
(4) 7/10
Found 4 solutions by ikleyn, math_tutor2020, MathTherapy, greenestamps:Answer by ikleyn(52931) (Show Source):
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Dhruv bought some white sugar and some brown sugar.
He used an equal amount of white and brown sugar.
He had 3/5 of the while sugar and 1/2 of the brown sugar left.
What fraction of the sugar which Dhruv bought was used?
(1) 4/7
(2) 4/9
(3) 5/11
(4) 7/10
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Let "w" be the amount of the white sugar Dhruv bought.
Let "b" be the amount of the brown sugar Dhruv bought.
He used and .
From the problem, we have this equation
= ("He used an equal amount of white and brown sugar"),
or 0.4*w = 0.5*b. (1)
They want you calculate this ratio
. (2)
From (1), express w = = 1.25*b and substitute it into (2). You will get
= = = = = = .
ANSWER. The fraction of the sugar Dhruv used was of the total amount of the sugar.
He has 3/5 of the white sugar left over, so 2/5 of it was used.
He also used up 1/2 of the brown sugar.
Normally when it comes to fractions we try to get the denominators to be the same (often the LCD).
In this rare case, I'll make the numerators equal to a common multiple.
I'll go with 2 as this common numerator.
2/5 stays the same
1/2 becomes 2/4
Dhruv used 2/5 of the white sugar and 2/4 of the brown sugar.
The reason I made the numerators the same was because he used an equal amount of sugar from each type.
So that's why I want those '2's to match up.
He used up 2+2 = 4 parts of sugar out of 5+4 = 9 parts total.
Therefore we arrive at 4/9 to represent the fractional amount of sugar used.
Dhruv bought some white sugar and some brown sugar. He used an equal amount of white and brown sugar. He had 3/5 of the while sugar and 1/2 of the brown sugar left. What fraction of the sugar which Dhruv bought was used?
(1) 4/7
(2) 4/9
(3) 5/11
(4) 7/10
Let amount of white and brown bought, be W and B, respectively
As of white (W) remained, he used of the white (W), or
As of brown (B) remained, he used of the brown (B), or
Since the same amount of white and brown was used, then we get:
5B = 4W ------ Cross-multiplying
Total amount used:
Total amount bought:
Fraction of total amount bought thatw's used:
(