The length of a rectangle is 3
inches less than
3
times the width. The perimeter is
106
inches. Find the length and the width

Let us say that x = length of rectangle and y = width of rectangle. It says that length is 3 inches less than twice the width. Twice the width means two times the width, so this is 2y, and 3 less means subtract 3, so the length is 2y-3. You can write this as x = 2y-3.  

They give you the perimeter of the rectangle. Remember that perimeter means adding up all of the sides of the rectangle. The sides of the rectangle are x, x, y, and y, so we add all these together to get the perimeter.  

                   length = x

          |                            |

     y   |                            |  width = y

          |                            |

                       x

Perimeter is  x+x+y+y = 2x+2y = 18. Next, we plug in x, since we know that x = 2y-3:

2(2y-3)+2y =18

Use the distributive property to do 2(2y-3) = 2*2y-2*3 = 4y-6. So we have

4y-6+2y = 18.  Combine like terms 4y and 2y to get 6y.

6y-6 = 18.  Add 6 to both sides to solve for 6y

6y = 24.   Divide by 6 to solve for y

y = 4.  So this is your width.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls