The greater of the two numbers whose product is 900 and sum exceeds their difference by 30 is

Options

A. a) 60
B. b) 75
C. c) 90
D. d) 100

Answer

To solve the problem, we need to find two numbers \( x \) and \( y \) such that:

1. Their product \( xy = 900 \)
2. Their sum \( x + y \) exceeds their difference \( x - y \) by 30, which can be expressed as \( x + y = (x - y) + 30 \)

Let's solve this step by step.

### Step 1: Set up the equations

From the problem, we have two equations:

1. \( xy = 900 \) (Equation 1)
2. \( x + y = (x - y) + 30 \) (Equation 2)

### Step 2: Simplify Equation 2

We can rearrange Equation 2:

\[ x + y = x - y + 30 \]

Subtract \( x \) from both sides:

\[ y = -y + 30 \]

Now, add \( y \) to both sides:

\[ 2y = 30 \]

Dividing both sides by 2 gives:

\[ y = 15 \]

### Step 3: Substitute \( y \) back into Equation 1

Now that we have \( y = 15 \), we can substitute this value into Equation 1:

\[ x \cdot 15 = 900 \]

Dividing both sides by 15 gives:

\[ x = \frac{900}{15} = 60 \]

### Step 4: Identify the greater number

Now we have both numbers:

- \( x = 60 \)
- \( y = 15 \)

The greater of the two numbers is:

\[ \text{Greater number} = 60 \]

### Final Answer

The greater of the two numbers is **60**.

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