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Sagot :
the number of students is 24000
the number of professors is 1500
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
[tex]x=16y\Rightarrow equation(1)[/tex]b)together the students and professors number 25,600, so
[tex]x+y=25500\Rightarrow equation(2)[/tex]Step 2
solve the equations
[tex]\begin{gathered} x=16y\Rightarrow equation(1) \\ x+y=25500\Rightarrow equation(2) \end{gathered}[/tex]a) replace the x valur from equation (1) into equation (2)
[tex]\begin{gathered} x+y=25500 \\ \text{replace} \\ (16y)+y=25500 \\ 17y=25500 \\ \text{divide both sides by 17} \\ \frac{17y}{17}=\frac{25500}{17} \\ y=1500 \end{gathered}[/tex]therefore,
the number of professors is 1500
b) now, replace the y value into equation(1) to find x
[tex]\begin{gathered} x=16y\Rightarrow equation(1) \\ x=16\cdot1500 \\ x=24000 \end{gathered}[/tex]therefore, the number of students is 24000
I hope this helps you
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