there are 267 students and teachers in a school. the ratio of students to teachers is 25:2 . How many students and teachers are there?

s/t=25/2

s= 12.5 t

but s+t=267
solve for s, t

what does that mean........

To solve this problem, you can set up a proportion using the ratio of students to teachers in the school.

The ratio of students to teachers is given as 25:2.

Let's assign variables to the number of students and teachers.

Let S represent the number of students.
Let T represent the number of teachers.

Since the ratio of students to teachers is 25:2, we can write the proportion:

S/T = 25/2

Cross-multiplying the proportion:

2S = 25T

Now, we know that there are 267 students and teachers in total in the school.

So we can write another equation:

S + T = 267

Now we have a system of equations:

2S = 25T
S + T = 267

To solve the system, we can substitute the value of S from the second equation into the first equation.

Solve the second equation for S:

S = 267 - T

Substitute this value of S into the first equation:

2(267 - T) = 25T

Simplify:

534 - 2T = 25T

Now, solve for T:

Combine like terms:

534 = 27T

Divide both sides by 27:

T = 534 / 27

Simplify:

T ≈ 19.78

Since you can't have a fraction of a teacher, we can round up to the nearest whole number, so T = 20.

Now, substitute the value of T back into the second equation to find S:

S + 20 = 267

Solve for S:

S = 267 - 20

S = 247

Therefore, there are 247 students and 20 teachers in the school.