# Glasses

There are 36 pupils in the class. Nine girls wear glasses. Boys with glasses are five less than girls without glasses. Boys without glasses are two times more than girls without glasses. How many boys and how many girls?

c =  19
d =  17

### Step-by-step explanation:

c+d = 36
d = 9 + f
c = a + b
a = f - 5
b = 2 f

c+d = 36
d = 9 + f
c = a + b
a = f - 5
b = 2·f

c+d = 36
d-f = 9
a+b-c = 0
a-f = -5
b-2f = 0

Pivot: Row 1 ↔ Row 3
a+b-c = 0
d-f = 9
c+d = 36
a-f = -5
b-2f = 0

Row 4 - Row 1 → Row 4
a+b-c = 0
d-f = 9
c+d = 36
-b+c-f = -5
b-2f = 0

Pivot: Row 2 ↔ Row 4
a+b-c = 0
-b+c-f = -5
c+d = 36
d-f = 9
b-2f = 0

Row 5 + Row 2 → Row 5
a+b-c = 0
-b+c-f = -5
c+d = 36
d-f = 9
c-3f = -5

Row 5 - Row 3 → Row 5
a+b-c = 0
-b+c-f = -5
c+d = 36
d-f = 9
-d-3f = -41

Row 5 + Row 4 → Row 5
a+b-c = 0
-b+c-f = -5
c+d = 36
d-f = 9
-4f = -32

f = -32/-4 = 8
d = 9+f = 9+8 = 17
c = 36-d = 36-17 = 19
b = -5-c+f/-1 = -5-19+8/-1 = 16
a = 0-b+c = 0-16+19 = 3

a = 3
b = 16
c = 19
d = 17
f = 8

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