Two numbers are in the ratio of 5:6. If 7 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers.

To solve the problem, let's denote the two numbers as 5x and 6x, where x is a common multiplier.

Setting Up the Equation

According to the problem, when we subtract 7 from each number, the new ratio becomes 4:5. This can be expressed mathematically as:

(5x - 7) / (6x - 7) = 4 / 5

Cross-Multiplying

To eliminate the fraction, we can cross-multiply:

5(5x - 7) = 4(6x - 7)

Expanding Both Sides

Now, let's expand both sides of the equation:

• 25x - 35 = 24x - 28

Solving for x

Next, we can isolate x:

• 25x - 24x = -28 + 35
• x = 7

Finding the Numbers

Now that we have the value of x, we can find the original numbers:

• First number: 5x = 5 * 7 = 35
• Second number: 6x = 6 * 7 = 42

Final Answer

The two numbers are 35 and 42.