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.