Write a system of equations for given the situation. Include your let statements: The length of a rectangle is three more than six times the width. The perimeter of the entire rectangle is 42 meters.

Question

I really need help with this

Answer 1

The length is 6w+3 where w is the width.

The perimeter is 2* Length + 2*width

42 = 2(6w+3) + 2w

42 = 12w + 6 + 2w

42 = 14w + 6

36 = 14w

36/14 = w

w = 18/7

The width is 18/7.

THe length is 6(18/7)+3 =

6*18 / 7 + 3/1 = <--- multiplies the fractions; also 3 = 3/1

6*18/ 7 + 21/ 7 <--- common denominator is 7; So 3/1 = 21/7

108/7 + 21/7 =

129/7

The width is 18/7 = 2 and 4/7

The length is 129/7 = 18 and 3/7

The perimeter is 2(18/7) + 2(129/7) =

(36 + 258)/7 =

294/7 =

42

Yes, it checks!