Givens
The ratio give is 7 (black) to 2 white)
The total number of beads is 54
Ratio
The best way to do this is to change the ratio to Black: Total
The total number of beads can be represented by 9 as the denominator in the ratio.
Black to total = 7 / 9
Formula
7/9 = x / 54 where x is the number of black beads.
Solution
Multiply both sides by 54
7/9 * 54 = x/54*54 Simplify
7 * 6 = x 9 goes into 54 six times. Combine the right
42 = x
Number of beads by color.
Black: 42
White: 54 - 42 = 12
Answer
There are 42 - 12 = 30 more black beads than white.