if (x+y)/x=4 and (y+z)/z=5. what is th value of x/z?

Question

how do you solve this?

Answer 1

Since you are trying to find x/z, you're going to want to solve the first equation for x and solve the second equation for z.

For the first equation, you have:

(x+y)/x = 4 ------- multiply both sides by x
x+y = 4x ---------- subtract 4x from both sides
x+y-4x = 0 ------- collect like terms
-3x+y = 0 -------- subtract y from both sides
-3x = -y ----------- divide both sides by -3
x = y/3

Now, for the second equation you have:

(y+z)/z = 5 ------- multiply both sides by z
y+z = 5z ---------- subtract 5z from both sides
y+z-5z = 0 ------- collect like terms
y-4z = 0 ---------- subtract y from both sides
-4z = -y ----------- divide both sides by -4
z = y/4

Now, you know x = y/3 and you know z = y/4, so
x/z = (y/3)/(y/4) = (y/3)*(4/y) = 4/3

x/z = 4/3

Answer 2

4/3

Answer 3

fors distribute the denominator to get:
x/x + y/x=4 1+ y/x=4 y/x = 3
flip both sides so
x/y=1/3
do the same for the 2nd term
y/z= 4 and z/y=1/4

now
x/y / z/y = 1/3 / 1/4= x/z = 1/3 *4/1=4/3

Answer 4

(x + y)/x = 4 => x = y/3

y + z/z = 5 => z = y/4

x/z = (y/3)/(y/4) = 4/3

Answer 5

(x+y)/x=4
x/x + y/x = 4
1 + y/x = 4
y/x = 3
y/3 = x

(y+z)/z=5
y/z + z/z = 5
y/z + 1 = 5
y/z = 4
y/4 = z

So,
x/z = (y/3)/(y/4) = 4y/3y = 4/3

Answer 6

first one, x+y=4x, y=3x, y/3=x
second one, y+z=5z, y=4z, y/4=z

x/z=(y/3)/(y/4)
=(y/3)*(4/y)
=4/3