Two numbers are in the ratio `4:5` and their sum is 189. Find the numbers.

Answer

To solve the problem step by step, we will break down the process of finding the two numbers that are in the ratio of 4:5 and whose sum is 189.

### Step 1: Understand the ratio
The ratio of the two numbers is given as 4:5. This means that if we let the first number be represented as 4 parts, the second number will be represented as 5 parts.

### Step 2: Define the numbers
Let the first number be \( 4x \) and the second number be \( 5x \), where \( x \) is a common multiplier.

### Step 3: Set up the equation for the sum
According to the problem, the sum of the two numbers is 189. Therefore, we can write the equation:
\[ 4x + 5x = 189 \]

### Step 4: Simplify the equation
Combine like terms on the left side:
\[ 9x = 189 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 9:
\[ x = \frac{189}{9} \]
Calculating this gives:
\[ x = 21 \]

### Step 6: Find the first number
Now that we have \( x \), we can find the first number:
\[ \text{First number} = 4x = 4 \times 21 = 84 \]

### Step 7: Find the second number
Next, we find the second number:
\[ \text{Second number} = 5x = 5 \times 21 = 105 \]

### Step 8: State the final answer
The two numbers are:
- First number: 84
- Second number: 105

### Summary
The numbers in the ratio of 4:5 that add up to 189 are 84 and 105.

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