Aseed company sells two grades of seed. a 100-pound bag of a mixture of rye and kentucky bluegrass sells for $235, and a 100-pound bag of bluegrass sells for $341. how many bags of each are sold in a week when the receipts for 17 bags are $4,949?

The company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass

Step-by-step explanation:

This is a classical problem that can be solved using a system of equations:

Let us first define our variables:

as the number of 100-pound bags which contain a mixture of rye and Kentucky bluegrass and,

as the number of 100-pound bags of bluegrass.

The problem tells us that in a week a total of 17 bags were sold, therefore, we can say that this number must be equal to the number of bags containing the mixture of rye and Kentucky bluegrass plus the number of bags containing bluegrass. Then, according to our variable names:

  (1)

The problem also says that the company got a receipt for $4,949 in total. Hence, this number has to be equal to the total number of bags that contain rye and Kentucky bluegrass seeds times its price plus the number of bags containing bluegrass multiplied by its price. Then,

 (2)

Now we have the system of equations:

  (1)

 (2)

Solving for in equation (1)

  (3)

And substituting in equation (2)

Then, substituting in equation (1):

Thus, the company sold 8 bags of a mixture of rye and Kentucky bluegrass and 9 bags of bluegrass.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584