distributive property

Question

A rectangular field is 850 feet wide. One portion of the field is 6y feet long. The other portion of the field is 15x feet long. Use the distributive property to find an expression for the area of this field

Next assume x = 50 feet and the area of the entire field is 943500 square feet . Find the length and area of each portion of the field.

Answer 1

Since length times width equals area we can express the area of the entire field by adding the lengths of the two portions of the field and multiplying by the area as in the expression:

850(6y + 15x) = Area

If we know that the area is 850000 square feet and we know that x = 50 feet we can rewrite the expression as:

850(6y + 15*50) = 943500

simplify to

850(6y + 750) = 943500

Now we have only one variable which we can solve for.

Distrubute the 850 to by multiplying it by both terms inside of the parentheses to get

5100y + 637500 = 943500

subtract 637500 from both sides to get:

5100y = 306000

divide both sides by 5100

y = 60

Now substitute y back into the original equation:

850(60*6 + 750) = 943500

850(360 + 750) = 943500

By multiplying this we can see it checks out.

943500 = 943500

Now we need to find the area and length of each portion of the field

So length of section 1 = 360 feet

Length of section 2 = 750 feet

 

Area of section 1 = 850 x 360 = 306000 square feet

Area of section 2 = 850 x 750 = 637500 square feet

Answer 2

64/4=(40+_) /4

  =(_ /4)+(_ /_)

  =_+ 6

  = _

Answer 3

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12+4