Tha difference between two whole numbers is 66.Tha ratio of the two numbers is 2:5.what are the two numbers?

Let's assume the smaller number is x and the larger number is y.

According to the given information, the difference between the two numbers is 66, so we can write the equation:

y - x = 66 ...(1)

The ratio of the two numbers is given as 2:5, which means:

x/y = 2/5

To solve for the two numbers, we can use the concept of cross-multiplication:

5x = 2y ...(2)

Now, we have a system of two equations (equations 1 and 2) with two variables (x and y). We can solve this system of equations to find the values of x and y.

Multiplying equation (2) by 3, we get:

15x = 6y ...(3)

Now, we can subtract equation (1) from equation (3):

15x - (y - x) = 6y - 66
15x - y + x = 6y - 66
16x - y = 6y - 66
16x = 7y - 66
16x - 7y = -66 ...(4)

Now, we have a new equation (equation 4) with two variables (x and y). We can solve this equation to find the values of x and y.

Using trial and error, we can find that when x = 12 and y = 30, the equation is satisfied:

16(12) - 7(30) = -66
192 - 210 = -66
-18 = -66

Therefore, the two numbers are 12 and 30.

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