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

Our linear equations calculator calculates it.



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Do you have a system of equations and are looking for calculator system of linear equations?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: