Answer:
y = 60
Step-by-step explanation:
<h3>Step 1: Make sense of the given</h3>
"The ratio of y to x is 3"
This means that, ![y\div x=3](https://tex.z-dn.net/?f=y%5Cdiv%20x%3D3)
"The sum of y and x is 80"
This means, ![x+y=80](https://tex.z-dn.net/?f=x%2By%3D80)
<h3>Step 2: Make use of the facts</h3>
If
, then
.
We can plug this into the other equation by substitution:
![x + (3 * x)=80](https://tex.z-dn.net/?f=x%20%2B%20%283%20%2A%20x%29%3D80)
This simplifies to:
![4x = 80](https://tex.z-dn.net/?f=4x%20%3D%2080)
Which we can solve out and get:
.
<h3>Step 3: Plug and Chug</h3>
We solved for x, but we need the value of y.
So, we go back to the equation we first derived: "
".
And now we substitute the value of x, into this.
![y = (3 * (20))](https://tex.z-dn.net/?f=y%20%3D%20%283%20%2A%20%2820%29%29)
By solving this out, we get:
![y=60](https://tex.z-dn.net/?f=y%3D60)
So, the value of y is 60.