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QuestionSolve x+y2x+3y=38\frac{x+y}{2x+3y}=\frac{3}{8} and x+2y=225x+2y=225 for xx and yy.

Studdy Solution

STEP 1

Assumptions1. The given equation is x+yx+3y=38\frac{x+y}{x+3y}=\frac{3}{8}. . Another given equation is x+y=225x+y=225.
3. We need to find the values of xx and yy.

STEP 2

First, we can simplify the first equation by multiplying both sides by 8(2x+y)8(2x+y) to eliminate the fraction.
8(x+y)=(2x+y)8(x+y) =(2x+y)

STEP 3

Now, we can distribute the numbers on both sides of the equation to simplify it further.
8x+8y=6x+9y8x+8y =6x+9y

STEP 4

Rearrange the equation to isolate xx on one side.
8x−6x=9y−8y8x -6x =9y -8y

STEP 5

implify the equation to get the value of xx in terms of yy.
2x=y2x = y

STEP 6

We can substitute 2x2x with yy in the second given equation x+2y=225x+2y=225.
y+2y=225y +2y =225

STEP 7

implify the equation to solve for yy.
3y=2253y =225

STEP 8

Divide both sides by3 to get the value of yy.
y=2253y = \frac{225}{3}

STEP 9

Calculate the value of yy.
y=2253=75y = \frac{225}{3} =75

STEP 10

Now that we have the value of yy, we can substitute it into the equation 2x=y2x = y to find the value of xx.
2x=752x =75

STEP 11

Divide both sides by to get the value of xx.
x=75x = \frac{75}{}

STEP 12

Calculate the value of xx.
x=752=37.5x = \frac{75}{2} =37.5The values of xx and yy are 37.537.5 and 7575 respectively.

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