Question

For Sophia’s graduation party, several tables of the same width will be arranged end to end to form a serving table with a total area of 75 ft 2 . The total length of the tables will be two more than three times the width. Find the length and width of the serving table so that Sophia can purchase the correct table cloth. Round your answers to the nearest tenth

Answer 1

The length and width of the serving table is 16.1 ft and 4.7 ft respectively.

Explanation:

Consider the provided information.

Let the width of the table is x and length of the table is y.

The total length of the tables will be two more than three times the width.

This can be written as:

y = 2+3x

The area of the table is 75 ²ft

The area of rectangle is:

length × width = Area

Substitute width = x and length = 2+3x in above formula.

(x)(2+3x) = 75

2x+3x²-75 = 0

3x²+2x-75 = 0

The above equation is in the form of ax²+bx+c=0. Now use the quadratic formula to find the root of the equation.

`x_(1,2)=(-b\pm√(b^2-4ac))/(2a)`

Substitute a=3, b=2 and c=-75 in above formula.

`x_(1,2)=(-2\pm√(2^2-4(3)(-75)))/(2(3))`

`x_(1,2)=(-2\pm√(904))/(6)`

`x_(1,2)=(-2\pm30.07)/(6)`

`x_(1)=(-2+30.07)/(6)`

Ignore the negative value of x as width should be a positive number.

`x=4.7\ ft`

Now substitute the value of x in y = 2+3x.

y = 2+3(4.7)

y = 16.1 ft

Hence, the length and width of the serving table is 16.1 ft and 4.7 ft respectively.

Answer 2

The length is 16.1 ft and the width is 4.7 ft

Explanation:

Let

x -----> the total length of the tables

y -----> the width of the tables

we know that

The area is equal to

`A=xy`

`A=75\ ft^(2)`

so

`75=xy` -----> equation A

`x=3y+2` -----> equation B

substitute equation B in equation A

`75=(3y+2)y`

`3y^(2) +2y-75=0`

Solve the quadratic equation by graphing

The solution is
`y=4.7\ ft`

Find the value of x

`x=3(4.7)+2=16.1\ ft`

therefore

The length is 16.1 ft and the width is 4.7 ft