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Alex
3 years ago
9

There are 18 boys in a class there are w fewer boys than girls how many students are there in the class

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
6 0
The Number of boys in the class is: 18

 Let's call "g" to the number of girls in the class.

 The problem says that there is "w" fewer boys than girls, so we have:

 g-w=18

 Then, the number of girls in the class  is:

 g=18+w

 Let's call "x" to the total number of studens in the class:

 x=g+18

 When we substitute g=18+w  into x=g+18, we obtain:

 x= (18+w)+18

 The total number of studens in the class is:

 x=w+36
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Step-by-step explanation:

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natali 33 [55]

To solve this problem, we need to know 2 relationships:

<h2>1. AC = AB + BC</h2>

The distance of AC is the sum of AB and BC.

AC = AB + BC

We know this since the distance of going from A to C (AC) is the same as going from A to B (AB), then B to C (BC).

<h2>2. AB = BC</h2>

The distance of AB is the same as AC.

AB = BC

We know this since B is in the middle of AC, so the distance from B to A (BA) is the same as the distance from B to C (BC).

You can see the attached image (at the bottom) for a visualization of this.

<h2>Putting them together</h2>

Since we know the values of AB and BC...

AB = x+9\\BC = 3x-7

...we can put these values into our 2nd equation and solve for x:

AB = BC\\x + 9 = 3x -7

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x + 16 = 3x

Subtract x from both sides:

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Divide both sides by 2:

8 = x\\x = 8

Knowing x, we can find the distance of AC using our first equation.

AC = AB + BC

Let's put in the values of AB and BC:

AC = (x+9) + (3x-7)

Before we put in x = 8, we can simplify this:

AC = (x+9) + (3x-7)\\AC = x + 9 + 3x -7\\AC = x + 3x + 9 -7\\AC = 4x + 9 - 7\\AC = 4x+2

We group x and 3x and add those together. Then we subtract 7 from 9.

With this equation, we can put in x = 8:

AC = 4x +2\\AC = 4*8 + 2

Since 4 * 8 = 32:

AC = 4 * 8 + 2\\AC = 32 + 2\\AC = 34

Finally, we have found both x and AC.

<h2>Answer</h2>

x = 8

AC = 34

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