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madreJ [45]
3 years ago
10

A school board has determined that there should be 4 teachers for every 50 students. How many teachers are needed for an enrollm

ent of 2,650 students?
Mathematics
2 answers:
Dimas [21]3 years ago
7 0

Answer:

212 teachers are needed for an enrollment of 2,650 students.

Step-by-step explanation:

This is a kind of question that can be solved using <em>proportions. </em>

<em>Proportions</em> are used when we are asked about finding one unknown value, knowing the value of others that keep a <em>ratio</em> among all of them, including the unknown value.

In this case, we know that a school board estimated that 4 teachers are needed for every 50 students:

\\ \frac{4_{teachers} }{50_{students}}=ratio  

If we divide 4 teachers by 50 students, we obtained a <em>ratio</em>, or a constant relationship that remains between teachers and students, that is, how many teachers are needed for the number of students, or more generally "<em>how many times the first number contains the second</em>" [Wikipedia, 2019].

We can also notice that more students require more teachers (which is a relation of <em>direct proportionality</em>), that is, if we require more students, more teachers are also required in the same ratio or constant already mentioned.

Then, we can make a proportion among these values because they keep the same ratio of teachers to students (but can also be students to teachers).

So, we can pose the following question:

If four (4) teachers are needed for every 50 students, how many teachers are needed to attend 2,650 students? Then,

\\ \frac{4_{teachers}}{50_{students}} = \frac{X_{teachers}}{2650_{students}} = <em>the same ratio or constant</em>.

To know the amount of teachers needed for 2,650 students:

\\ X_{teachers} = \frac{2650_{students} * 4_{teachers} }{50_{students}}.

or,

\\ X_{teachers} = \frac{2650 * 4_{teachers} }{50}.

\\ X_{teachers} = 212_{teachers}.

So, for an enrollment of 2,650 students there should be 212 teachers, according to the ratio (teachers/students) previously determined by the school board.

lozanna [386]3 years ago
6 0
I believe the answer is 53 but im not 100% sure

4:50
x:2650

2650/50=53
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