MATH ALGEBRA HELP!!?

Question

1.There are five times as many $1 bills as $2 bills. The total number of bills is 48. How many $1 bills are there?

2.The perimeter of a rectangle is 168 cm. Its length is five times its width. Find the length and width.

3.The width of a rectangle is 5 meters less than the length. Find the dimensions of the rectangle if its perimeter is 90 meters.

Please explain if you can. Thank you.

Answer 1

1.  let x = # of $2 bills

therefore the number of $1 bills will be:  5*x = 5x

then we will have the equation for the total number of bills as:

x + 5x = 48

6x = 48

and x = 8

# of $2 bills = 8

# of $1 bills:  5*8 = 40

2.  let  x = the width of the rectangle

therefore the length is: 5*x = 5x

the perimeter of the rectangle will then be represented by the equation:

2(x + 5x) = 168

solving for x we have:

2(6x) = 168

12x = 168

then x = 14

so, the width is = 14cm and the length is: 5*14 = 70cm

3.  let x = the length of the rectangle

therefore the width of the rectangle is: x - 5

the perimeter of the rectangle will then be represented by the equation:

2[x + (x - 5)] = 90

solving for x we have:

2(2x - 5) = 90

4x - 10 = 90

4x = 100

then x = 25

the length of the rectangle = 25 cm

the width of the rectangle is: 25 - 5 = 20cm

hope this helps!!!

Answer 2

1. Forty $1 bills

    

    x = # $1 bills

    y = # $2 bills

    x = 5y

    x + y = 48    

    x + y = 48

    (5y) + y = 48

    6y = 48

    y = 8            

        

    x = 5y

    x = 5(8)

    x = 40            

2. Length = 70 cm ; Width = 14 cm

    

    x = length of rectangle

    y = width of rectangle

    x = 5y

    2x + 2y = 168 cm

    2x + 2y = 168

    2(5y) + 2y = 168

    10y + 2y = 168

    12y = 168

    y = 14        

    x = 5y

    x = 5(14)

    x = 70        

    

3. Length = 25 m ; Width = 20 m

    x = length of rectangle

    y = width of rectangle

    x = y + 5

    2x + 2y = 90 m

    2x + 2y = 90

    2(y + 5) + 2y = 90

    2y + 10 + 2y = 90

    4y + 10 = 90

    4y = 80

    y = 20        

    x = y + 5

    x = 20 + 5

    x = 25