# Students

If the fifth-grade class left 20% of students and in the seventh grade were added two pupils, in the eighth one pupil, the number has not changed in the ninth grade, but it is now tenth students less than it was in the fifth grade.

How many pupils are in the 9th grade now?

d =  27

### Step-by-step explanation:

b=a - 0.20 a
c = 2+b
d = c+1
d = a - 0.10a

b=a - 0.20·a
c = 2+b
d = c+1
d = a - 0.10·a

0.8a-b = 0
b-c = -2
c-d = -1
0.9a-d = 0

Pivot: Row 1 ↔ Row 4
0.9a-d = 0
b-c = -2
c-d = -1
0.8a-b = 0

Row 4 - 0.8/0.9 · Row 1 → Row 4
0.9a-d = 0
b-c = -2
c-d = -1
-b+0.8889d = 0

Row 4 + Row 2 → Row 4
0.9a-d = 0
b-c = -2
c-d = -1
-c+0.8889d = -2

Row 4 + Row 3 → Row 4
0.9a-d = 0
b-c = -2
c-d = -1
-0.1111d = -3

d = -3/-0.11111111 = 27
c = -1+d = -1+27 = 26
b = -2+c = -2+26 = 24
a = 0+d/0.9 = 0+27/0.9 = 30

a = 30
b = 24
c = 26
d = 27

Our linear equations calculator calculates it.

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Showing 1 comment:
Math student
someone do it!

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