Question

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

Answer 1

Answer:

Two positive numbers are 400, 250

Step-by-step 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

$\frac{x}{y} =\frac{8}{5}$

Multiply by y on both sides

$x =\frac{8}{5}y$ -------------> first equation

The difference of two numbers is 150

$x-y = 150$

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

$\frac{8}{5} y - y = 150$

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

$x =\frac{8}{5}y$

$x =\frac{8}{5}(250)=400$

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 $\frac{x}{y} = \frac{8}{5}$ and x-y=150. Combining these two equations, we can make a system of equations $\left \{ {{\frac{x}{y} = \frac{8}{5} } \atop {x-y=150}} \right.$. Solving this system, we find that x=400 and y=250