Question

In a college there are 16 times as many students as professors. If together the students and professors number 25,500, how many students are there in the college?The number of students in the college is

Answer 1

the number of students is 24000

the number of professors is 1500

Step-by-step explanation

Step 1

set the equations:

Let

x represents the number of students

y represents the number of professors

now, traslate the worid into expressions

a) there are 16 times as many students as professors( in other words, you have to multiply the number of professors by 16 to obtain the number of students),so

`x=16y\Rightarrow equation(1)`

b)together the students and professors number 25,600, so

`x+y=25500\Rightarrow equation(2)`

Step 2

solve the equations

`\begin{gathered} x=16y\Rightarrow equation(1) \\ x+y=25500\Rightarrow equation(2) \end{gathered}`

a) replace the x valur from equation (1) into equation (2)

`\begin{gathered} x+y=25500 \\ \text{replace} \\ (16y)+y=25500 \\ 17y=25500 \\ \text{divide both sides by 17} \\ (17y)/(17)=(25500)/(17) \\ y=1500 \end{gathered}`

therefore,

the number of professors is 1500

b) now, replace the y value into equation(1) to find x

`\begin{gathered} x=16y\Rightarrow equation(1) \\ x=16\cdot1500 \\ x=24000 \end{gathered}`

therefore, the number of students is 24000

I hope this helps you