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SAT官方每日一题附答案和解析[数学](2018年11月23日)
日期:2018-11-23 09:35

(单词翻译:单击)

每日一题

Mathematics

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 of the 50% solution with ymL 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.

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重点单词
  • obtainvt. 获得,得到 vi. 通用,流行,存在
  • eliminatev. 除去,剔除; 忽略
  • solutionn. 解答,解决办法,溶解,溶液
  • pharmacistn. 药剂师,药商
  • availableadj. 可用的,可得到的,有用的,有效的
  • equationn. 相等,方程(式), 等式,均衡
  • certainadj. 确定的,必然的,特定的 pron. 某几个,某