Question

A group of 75 math students were asked whether they like algebra and whether they like geometry. A total of 45 students like algebra, 53 like geometry, and 6 do not like either subject. A 4-column table with 3 rows. The first column has no label with entries likes algebra, does not like algebra, total. The second column is labeled likes geometry with entries a, c, 53. The third column is labeled does not like geometry with entries b, 6, e. The fourth column is labeled total with entries 45, d, 75. What are the correct values of a, b, c, d, and e? a = 16, b = 29, c = 22, d = 30, e = 24 a = 29, b = 16, c = 30, d = 22, e = 24 a = 16, b = 29, c = 24, d = 22, e = 30 a = 29, b = 16, c = 24, d = 30, e = 22

Answer 1

Answer:

Step-by-step explanation:

Let x be the number of students that like both algebra and geometry. Then:

1. 45-x is the number of students that like only algebra;

2. 53-x is the number of students that like only geometry.

You know that 6 students do not like any subject at all and there are 75 students in total.

If you add the number of students that like both subjects, the number of students that like only one subject and the number of students that do not like any subject, you get 75.

Therefore,

$x+45-x+53-x+6=75.$

Solve this equation:

$104-x=75,\\\\x=104-75,\\\\x=29.$

You get that:

29 students like both subjects;

45-29=16 students like only algebra;

53-29=24 students like only geometry;

24+6=30 students do not like algebra;

16+6=22 students do not like geometry.

a = 29, b = 16, c = 24, d = 30, e = 22

The correct choice is D.

Answer 2

Answer:

The answer is D.

Step-by-step explanation: