Question

The sum of 5 times the width of a rectangle and twice its length is 26 units. The difference of 15 times the width and three times the length is 6 units. Write and solve a system of equations to find the length and width of the rectangle

Answer 1

Answer: length = 8 units

Width = 2 units

Step-by-step explanation:

Let the length of the rectangle be represented by L

Let the width of the rectangle be represented by W

The sum of 5 times the width of a rectangle and twice its length is 26 units. This means that

5W + 2L = 26 - - - - - - - - 1

The difference of 15 times the width and three times the length is 6 units. It means that

15W - 3L = 6 - - - - - - - - 2

The system equations are equation 1 and equation 2.

Multiplying equation 1 by 3 and equation 2 by 2, it becomes

15W + 6L = 78

30W - 6L = 12

Adding both equations,

45W = 90

W = 90/45 = 2

15W - 3L = 6

15×2 - 3L = 6

-3L = 6 - 30 = - 24

L = - 24/ -3 = 8