Question

A garden has a perimeter of 120 feet. The difference between the length and twice the width is 24 feet. Write a system of linear equations that represents his situation. Then solve the system to find the length and width of the garden.

Answer 1

Lets say the length is x and the width is y.

The perimeter is calculated by using 2x +2y=120 and we know that the difference of x and twice y is 24, x-2y=24 so, lets use this and solve for x.

Add 2y to both sides and get x=2y+24. Now we can use substitution into the perimeter equation because we know what x equals.

 2(2y+24) +2y=120  Now solve for Y.

 4y+48+2y=120

6y+48=120

6y=72

y=12  Your width is 12feet. Now use twelve in your perimeter equation and solve for X

2x+2y=120 so,

2x +2(12)=120

2x+24=120  subtract 24 from both sides

2x=96  divide by 2

x=48  your length is 48 meters.