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

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23