SAT Mathematics Practice Test 3

Question : 44 of 58

Marks: +1, -0

Mr. Kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class?

Validate

Solution:

Let c be the number of students in Mr. Kohl’s class.
The conditions described in the question can be represented by the equations

n=3c+5

and

n+21=4c

.
Substituting

3c+5

for n in the second equation gives

3c+5+21=4c,

which can be solved to find

c=26

.
Choices A, B, and C are incorrect because the values given for the number of students in the class cannot fulfil both conditions given in the question.
For example, if there were 16 students in the class, then the first condition would imply that there are

3(16)+5=53

millilitres of solution in the beaker,
but the second condition would imply that there are

4(16)−21=43

millilitres of solution in the beaker.
This contradiction shows that there cannot be 16 students in the class.

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