Question

22 Lavinia Group. All Rights Reserved.This is a Lavinia Group™ product for RISE Summer School use only. Do not distribute.Story Problem Lesson 7:The school designed their rectangular vegetable garden to have aperimeter of 32 feet with the length measuring 2 feet more than twicethe width. Using y to represent the length of the garden and w torepresent its width, write and solve a system of equations that describesthis situation. What are the dimensions of the garden

Answer 1

We have that the length measuring 2 feet more than twice the width so this means

`y=2\cdot w+2`

all in feet, now we know that the perimeter is 32 feet so we have

`y+w=32`

Using the first equation and replacing in the second one we get

`(2\cdot w+2)+w=32`

this is

`\begin{gathered} 2w+2+w=32 \\ 3w+2=32 \\ 3w=32-2 \\ 3w=30 \\ w=(30)/(3)=10 \end{gathered}`

Replacing this in the first equation we get

`y=2\cdot(10)+2=20+2=22`

The answer is: the length of the garden is 22 and the width is 10 feet.