Question

A rectangular garden is 49 feet longer than it is wide. Its perimeter is 302 feet

a) let w be the width of the garden and L be the length. Write a system of linear equations whose solution gives the width and length of the garden.
b) Use the method of substitution to solve the system.

Answer 1

a)L+L+w+w=302

48+w+48+w+w+w=302

96+2w=302

2w=206

w=103

final answer: width is 103feet

length =L=48+w=48+103=151feet

Answer 2

The first equation would be w+49=l. The second equation would be 2w+2l=302. Now, substitute l in the second equation with the first equation and solve.

2w+2(w+49)=302
2w+2w+98=302
4w=204
w=51
l=51+49
l=100