SUM OF 2 NUMBERS IS 45 AND THE RATIO IS 7:8. FIND THE NUMBER.?

7n+8n=45
n(7+8)=45
n15=45
n=3
Numbers are
7n and 8n
7×3 and 8×3
21, 24

7+8 is 15
you want 45, i.e. 3 times as big, so use
21 + 24 = 45

When you want to split something into a ratio, you do this:

Add the numbers in the ratio: 7 + 8 = 15

Get two fractions, using the numbers in the ratio and the total: 7/15 and 8/15.

Apply those to the total
45 x 7/15 = 21
45 x 8/15 = 24

The results should add up to the total: 21 + 24 = 45

A lot of ratio problems are done like this.