MF graduate

78 school students graduate in mathematics or physics. Three times more students graduate from mathematics and do not graduate from physics than those who graduate from physics and do not graduate from mathematics. 69 students graduate in mathematics. How many students graduate from mathematics and physics?

Correct answer:

p =  42

Step-by-step explanation:


m+f+p=78
m=3f
m+p=69

m+f+p=78
m=3·f
m+p=69

f+m+p = 78
3f-m = 0
m+p = 69

Pivot: Row 1 ↔ Row 2
3f-m = 0
f+m+p = 78
m+p = 69

Row 2 - 1/3 · Row 1 → Row 2
3f-m = 0
1.333m+p = 78
m+p = 69

Row 3 - 1/1.33333333 · Row 2 → Row 3
3f-m = 0
1.333m+p = 78
0.25p = 10.5


p = 10.5/0.25 = 42
m = 78-p/1.33333333 = 78-42/1.33333333 = 27
f = 0+m/3 = 0+27/3 = 9

f = 9
m = 27
p = 42

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