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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

A doctor orders 300 milliliters(mL) of a certain medicine at a 40% solution. The pharmacy has the medicine available only in 50% and 25% solution. The pharmacist will mix xmL end text of the 50% solution with y mL end text of the 25% solution to obtain the desired 40% solution. Which of the following is the value of x?

A.40
B.120
C.180
D.260

答案和解析

答案：C

解析：

Choice C is correct. Since xmL of the 50% solution will be combined with ymL of the 25% solution to obtain 300mL of a 40% solution, it follows that x+y=300.
Since the pharmacist will mix xmL of the 50% solution and ymL of the 25% solution, the amount of actual medicine in the mixture is 0.5x+0.25y.
The doctor orders 300mL of the medicine at 40% solution. Which is (300)*(0.4)=120 milliliters of medicine.
Since the amount of actual medicine in the mixture must equal the amount of actual medicine in the end result, 0.5x+0.25y=120.
This all gives the following system of equations:
x+y=300
0.5x+0.25y=120
To find the value of x, eliminate y. Multiplying the first equation by -0.25 gives the following system:
-0.25x-0.25y=-75
0.5x+0.25y=120
Adding the two equations yields: 0.25x=45 And so x=180.