Question

Find two positive numbers if their ratio is 8:5 and the difference is 150.

Answer 1

Two positive numbers are 400, 250

Explanation:

Find two positive numbers if their ratio is 8:5 and the difference is 150.

LEt x and y are the two positive numbers

ratios is 8:5

`(x)/(y) =(8)/(5)`

Multiply by y on both sides

`x =(8)/(5)y` -------------> first equation

The difference of two numbers is 150

`x-y = 150`

Now we replace x with 8/5 *y (first equation)

`(8)/(5) y - y = 150`

Take LCD : 5, multiply each term by 5

`8y - 5y= 750`

Combine like terms

`3y= 750`

Divide by 3

`y=250`

Now plug in 250 for y and solve for x

`x =(8)/(5)y`

`x =(8)/(5)(250)=400`

so x= 400

Two positive numbers are 400, 250

Answer 2

We can set up a system and solve it. Let these numbers be x and y. We can write that
`(x)/(y) = (8)/(5)` and x-y=150. Combining these two equations, we can make a system of equations
`\left \{ {{(x)/(y) = (8)/(5) } \atop {x-y=150}} \right.`. Solving this system, we find that x=400 and y=250