Certainly! Let's tackle each part of the problem step-by-step.
### Part (a):
The ratio of two numbers is given as 4:5. We are also told that the first number is 20. We need to find the second number.
1. Let's denote the two numbers by [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
2. The ratio tells us that [tex]\( \frac{A}{B} = \frac{4}{5} \)[/tex].
Since the first number [tex]\( A \)[/tex] is 20, we can write:
[tex]\[ A = 20 \][/tex]
3. We can express [tex]\( B \)[/tex] in terms of [tex]\( A \)[/tex]:
[tex]\[ B = \frac{5}{4} \times A \][/tex]
4. Substituting [tex]\( A = 20 \)[/tex]:
[tex]\[ B = \frac{5}{4} \times 20 \][/tex]
5. Calculate [tex]\( B \)[/tex]:
[tex]\[ B = \frac{5}{4} \times 20 = 5 \times 5 = 25 \][/tex]
Therefore, the second number is [tex]\( 25 \)[/tex].
### Part (b):
The ratio of two numbers is given as 9:5. We are told that the second number is 45. We need to find the first number.
1. Let's denote the two numbers by [tex]\( X \)[/tex] and [tex]\( Y \)[/tex].
2. The ratio tells us that [tex]\( \frac{X}{Y} = \frac{9}{5} \)[/tex].
Since the second number [tex]\( Y \)[/tex] is 45, we can write:
[tex]\[ Y = 45 \][/tex]
3. We can express [tex]\( X \)[/tex] in terms of [tex]\( Y \)[/tex]:
[tex]\[ X = \frac{9}{5} \times Y \][/tex]
4. Substituting [tex]\( Y = 45 \)[/tex]:
[tex]\[ X = \frac{9}{5} \times 45 \][/tex]
5. Calculate [tex]\( X \)[/tex]:
[tex]\[ X = \frac{9}{5} \times 45 = 9 \times 9 = 81 \][/tex]
Therefore, the first number is [tex]\( 81 \)[/tex].
### Summary
- In part (a), the second number is [tex]\( 25 \)[/tex].
- In part (b), the first number is [tex]\( 81 \)[/tex].
