Of the 400 eighth-graders at pascal middle school, 117 take algebra, 109 take advanced computer, and 114 take industrial technology. furthermore, 70 take both algebra and advanced computer, 34 take both algebra and industrial technology, and 29 take both advanced computer and industrial technology. finally, 164 students take none of these courses. how many students take all three courses

If 164 of the 400 eighth-graders take none of these courses, then 400-164=236 students take some courses.

Let x students take all three courses, then:

1. 70-x take only both algebra and advanced computer,

2. 34-x take only both algebra and industrial technology,

3. 29-x take only both advanced computer and industrial technology.

Now let's count how many student take only one course:

1. 117-(x+34-x+70-x)=13+x take algebra,

2. 109-(x+29-x+70-x)=10+x take advanced computer,

3. 114-(x+29-x+34-x)=51+x take industrial technology.

Now count all students that take some courses:

51+x+10+x+13+x+29-x+34-x+70-x+x=236,

x=236-51-10-13-29-34-70,

x=29.

all three courses take 29 students.

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.

a:

step-by-step explanation:

a