Question

What is the ratio of x to y?

3/2 = 2x/2x+y

A. -3/2
B. -2/3
C. 2/3
D. 3/2

If you're confused of what the equation is, let me know and I'll take a screenshot of the question so it's easier. But, I'm thinking it's C.

Answer 1

is it
\[ \frac{3}{2} = \frac{2x}{2x+y} \]?

Answer 2

@phi Yes it is.

Answer 3

if you cross multiply, what do you get ?

Answer 4

x = 3y/2
y= 2x/3

Answer 5

try this
multiply both sides of
\[ \frac{3}{2} = \frac{2x}{2x+y} \]
by 2(2x+y)

Answer 6

So like this?

3 * 2x + y = 2 * 2x

Answer 7

almost, you need parens
3*(2x+y)= 4x
now distribute the 3

Answer 8

What do you mean distribute the 3?

Answer 9

3*(2x+y) means 3 times each term inside the parens

Answer 10

Sorry, I'm a bit confused but I got this when I times 3 by the terms in the parentheses.
y = 2x -3

Answer 11

3*(2x+y)= 4x

do 3*2x and 3*y

Answer 12

think of (2x+y) as a "package" and you have 3 packages
(so you have 3 of everything inside the package)

Answer 13

But how can I multiply it if I don't know what the variables are?

Answer 14

you multiply letters by just showing them being multiplied
example: x times y is x*y or xy
obviously we don't know what number that is, but we do know that it means x times y

Answer 15

3*(2x+y)= 4x

now distribute the 3 (i.e. multiply each term inside by 3)

Answer 16

So 3 x (2xy) ?

Answer 17

if it helps
say you had 3 farms, each had 2 cows and 1 horse
how many cows and horses do you have?

Answer 18

9?

Answer 19

how many of each type ?

Answer 20

6 cows and 3 horses.

Answer 21

yes

you did 3( 2 cows + 1horse) and got 3*2 cows + 3*1 horse

Answer 22

if we count x's and y's
3(2x + 1y) = 3*2 x + 3*1 y
or 6x+3y

Answer 23

see if you make sense of that. meanwhile
3*(2x+y)= 4x
6x+3y= 4x

now add -4x to both sides
6x-4x + 3y = 4x - 4x

on the right side, you have 4x take away 4 x's
on the left you have 6 x's take away 4 x's (or cows if you like)
that gives you

2x+3y= 0

Answer 24

So what do I do from here since I now have 0?

Answer 25

we want the ratio of x to y or x/y
so divide both sides by y
\[ \frac{2x+3y}{y}= \frac{0}{y} \\
\frac{2x}{y} + 3\frac{y}{y}= 0 \]

Answer 26

y/y is 1
so we have
\[ 2 \frac{x}{y}+3=0 \]
add -3 to both sides to get
\[ 2 \frac{x}{y}=-3\]
now divide both sides by 2

Answer 27

we could also do this
2x+3y= 0
3y= -2x (add -2x both sides)
now divide both sides by y
3 = -2 (x/y)
now divide both sides by -2
(3/-2) = x/y

or x/y = -3/2

Answer 28

So the answer is A?