Answer:
y = 20
Step-by-step explanation:
x+y+z = 50
x/y = 1/4 so y = 4x
Substitute y = 4x into x+y+z = 50
x + 4x + z = 50
5x + z = 50
y/z = 4/5 --> 4z = 5y so z =5/4 y
Substitute z =5/4 y into 5x + z = 50
5x + 5/4 y = 50
You can solve for x from these 2 equations
5x + 5/4 y = 50
y = 4x
Substitute y = 4x into 5x + 5/4 y = 50
5x + 5/4 (4x) = 50
5x + 5x = 50
10x = 50
x = 5
y = 4x = 4 (5) = 20
Answer
y = 20
The sum of the numbers x, y, and z is 50. The ratio of x to y is 1:4, and the ratio of y and z is 4:5
The value of y =20
Given :
The sum of the numbers x, y, and z is 50
The ratio of x to y is 1:4, and the ratio of y and z is 4:5.
The sum of the numbers x, y, and z is 50
The equation becomes [tex]x+y+z=50[/tex]
The ratio of x to y is 1:4
[tex]\frac{x}{y} =\frac{1}{4} \\4x=y\\y=4x[/tex]
Now use the second ratio . the ratio of y and z is 4:5
[tex]\frac{y}{z} =\frac{4}{5}\\5y=4z\\Replace \; y=4x\\5(4x)=4z\\20x=4z\\z=5x[/tex]
Replace y=4x and z=5x in the first equation
[tex]x+y+z=50\\x+4x+5x=50\\10x=50\\x=5[/tex]
Now we replace x with 5 and find out y
[tex]y=4x\\y=4(5)\\\y=20[/tex]
Learn more : brainly.com/question/23940720
