Answer :

edisonlara1212

Answer:

30 and 45

Step-by-step explanation:

So let's just define these two numbers as: x and y

We know these numbers aren't equal since the ratio isn't 1:1

Anyways, the ratio 3:2 really just means "for every 3 of x, there is two of y", this means that "y" is the bigger number since 2 y's are equal to 3 x's

Or in other words: 3x=2y

Since the sum of the two equations is 75, we can also derive the equation: x+y=75

Now all we have to really do is solve a linear systems of equations:

So let's solve by substitution:

[tex]x+y=75[/tex]

Subtract x from both sides

[tex]y=75-x[/tex]

[tex]3x=2y[/tex]

Substitute 75-x as y

[tex]3x=2(75-x)[/tex]

Distribute the 2

[tex]3x=150-2x[/tex]

Add 2x to both sides

[tex]5x=150[/tex]

Divide both sides by 5

[tex]x=30[/tex]

Now we can solve for y using either equation, but for me personally the x+y is easier to solve for y

[tex]30+y=75[/tex]

Subtract 30 from both sides

[tex]y=45[/tex]

So we have the two numbers, 30 and 45

Answer:

One number is 30 and the other number is 45

Step-by-step explanation:

[tex]\frac{x}{y} =\frac{3}{2}[/tex]  Cross multiply

2x = 3y

*2x -3y = 0

x + y = 75 Multiply this all the way through by -2 so that the x will cancel out.

(-2)(x + y) = 75(-2)

*-2x -2y = -150

* Add these two equations together.

-2x - 2y = 0

2x - 3y = -150

      -5x = -150  Divide both sides by -5

         x  = 30

Plug x into either equation to find y.

x + y = 75

30 + y = 75  Subtract 30 from both sides

y = 45

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