What is the sum of all possible values of y if x is a positive integer, xy > 0, and 6x+2y=25?
a 5
b 7
c 8
d 15
e 20

Option E

The sum of all possible values of y is 20

Solution:

Given that,

6x + 2y = 25

Where, xy > 0

We have to find the sum of all possible values of y if x is a positive integer

We can use values of x = 1, 2, 3, 4

For x = 5 and above, y will be negative

Substitute x = 1 in given equation

6(1) + 2y = 25

6 + 2y = 25

2y = 25 - 6

2y = 19

Divide both the sides of equation by 2

Substitute x = 2 in given equation

6(2) + 2y = 25

2y = 25 - 12

2y = 13

Divide both the sides of equation by 2

Substitute x = 3 in given equation

6(3) + 2y = 25

2y = 25 - 18

2y = 7

Divide both the sides of equation by 2

Substitute x = 4 in given equation

6(4) + 2y = 25

24 + 2y = 25

2y = 25 - 24

2y = 1

Divide both the sides of equation by 2

Now add all the values of "y"

Thus sum of all possible values of y is 20

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

d no solution

step-by-step explanation: