Question

the ratio of the number of people who own a smartphone to the number of people who own a flip phone is 4:3. if 500 more people own a smartphone than a flip phone,how many people own each type of phone?

Answer 1

Set up a proportion
$\frac{4}{3} = \frac{x+500}{x}$

Now, cross multiply to get
3x+1500=4x            Use inverse operations to simplify
-3x           -3x

x=1500

1500 people own a flip phone and 2000 own a smartphone

Answer 2

X - the number of people who own a smartphone
y - the number of people who own a flip phone

x:y=4:3
$\frac{x}{y}=\frac{4}{3} \\ 4y=3x \\ y=\frac{3}{4}x$

500 more people own a smartphone than a flip phone.
$x=500+y \\ x=500 + \frac{3}{4}x \\ x-\frac{3}{4}x=500 \\ \frac{1}{4}x=500 \\ x=500 \times 4 \\ x=2000 \\ \\ y=\frac{3}{4}x=\frac{3}{4} \times 2000=3 \times 500 =1500$

2000 people own a smartphone and 1500 people own a flip phone.