Verified answer

Step-by-step explanation:

Let's assume that the four consecutive multiples of 9 are x, y, z, and w, where:

x = 9a (the first multiple)

y = 9b (the second multiple)

z = 9c (the third multiple)

w = 9d (the fourth multiple)

where a, b, c, and d are consecutive integers.

We know that their sum is 270, so:

x + y + z + w = 270

Substituting the values of x, y, z, and w, we get:

9a + 9b + 9c + 9d = 270

Factoring out 9, we get:

9(a + b + c + d) = 270

Dividing both sides by 9, we get:

a + b + c + d = 30

Since a, b, c, and d are consecutive integers, we can express them in terms of a single variable. Let's assume that the first multiple is x = 9a, then the second multiple is y = 9(a+1), the third multiple is z = 9(a+2), and the fourth multiple is w = 9(a+3).

Substituting these values in the equation a + b + c + d = 30, we get:

a + (a+1) + (a+2) + (a+3) = 30

Simplifying the equation, we get:

4a + 6 = 30

Subtracting 6 from both sides, we get:

4a = 24

Dividing both sides by 4, we get:

a = 6

Therefore, the first multiple is:

x = 9a = 9(6) = 54

The second multiple is:

y = 9(a+1) = 9(7) = 63

The third multiple is:

z = 9(a+2) = 9(8) = 72

The fourth multiple is:

w = 9(a+3) = 9(9) = 81

So, the four consecutive multiples of 9 are 54, 63, 72, and 81.