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A snack mix that is 20% raisins is blended with a second mix

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A snack mix that is 20% raisins is blended with a second mix

by swerve » Fri Oct 05, 2018 1:39 pm

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A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pounds of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A. 25
B. 30
C. 35
D. 40
E. 50

The OA is C.

Source: EMPOWERgmat
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by deloitte247 » Sun Oct 07, 2018 12:23 pm
Let x =Additional pounds of first mix to be added
(20% * (5 + x)) + (30% * 10 ) = 22% * (15 + x )
$$\frac{20}{100}\cdot\left(5\ +\ x\right)+\ \frac{30}{100}\cdot\ 10=\frac{22}{100}\cdot\left(15\ +\ x\right)$$
0.2 * (5 + x) + 0.3 * 10 = 0.22 * (15 + x)
1 + 0.2x = 3.3 + 0.22x
0.2x - 0.22x = 3.3 - 4
$$\frac{\left(-0.02x\right)}{-0.02}=\ \frac{\left(-0.7\right)}{-0.02}$$
x = 35

Option C is CORRECT.
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by Scott@TargetTestPrep » Fri Oct 12, 2018 6:58 am
swerve wrote:A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pounds of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A. 25
B. 30
C. 35
D. 40
E. 50
The first mix has 5 x 0.2 = 1 lb of raisins and the second mix has 10 x 0.3 = 3 lb of raisins. If we let x = the additional number of pounds of the first mix that must be added to the initial blend to produce a blend of 22% raisins, then we have:

(1 + 3 + 0.2x)/(5 + 10 + x) = 22/100

100(4 + 0.2x) = 22(15 + x)

400 + 20x = 330 + 22x

70 = 2x

35 = x

Answer: C

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by fskilnik@GMATH » Fri Oct 12, 2018 11:55 am
swerve wrote:A snack mix that is 20% raisins is blended with a second mix that is 30% raisins. The initial blend is 5 pounds of the first mix and 10 pounds of the second. To make the final blend 22% raisins, how many additional pounds of the first mix must be added to the initial blend?

A. 25
B. 30
C. 35
D. 40
E. 50

Source: EMPOWERgmat
$$? = x$$
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Excellent opportunity for the Alligation (and Bruce Lee):

$$\frac{{10}}{{10 + \left( {5 + x} \right)}} = \frac{{22 - 20}}{{30 - 20}} = \frac{{2 \cdot \boxed5}}{{10 \cdot \boxed5}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,15 + x = 50\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,? = x = 35\,\,\,\,\,\,\,\,\left[ {{\text{pounds}}} \right]\,\,\,\,$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Portuguese-speakers :: https://www.gmath.com.br
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