Problem Solving

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

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.

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

$$? = x$$


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.