A fruit stand sells two varieties of strawberries: standard and deluxe. A box of standard strawberries sells for $7, and a box of deluxe strawberries sells for $13. In one day the stand sold 135 boxes of strawberries for a total of $1,275. How many boxes of each type were sold?

d = 55 boxes of deluxe

s = 135 - 55 = 80 boxes of standard

Step-by-step explanation:

This is a system of equations.

Let  s = number of standard boxes

     d = number of deluxe boxes

s + d = 135  sold

7s + 13d  = $1275

we can use substitution

s = 135 - d

7*(135 - d) + 13 d  = 1275

945 - 7d + 13d = 1275

6d = 330

d = 55 boxes of deluxe

s = 135 - 55 = 80 boxes of standard

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: