Question

HELP! URGENT!

Alice wrote three consecutive even numbers. The sum of these numbers was 252.

Pat wrote three consecutive odd numbers. Pat's numbers were larger than Alice's numbers.

The difference between the largest of Pat's numbers and the largest of Alice's numbers was 25.

What was the sum of Pat's numbers?

Answer 1

333

Explanation:

Let a represent Alice's numbers and p represent Pat's numbers.

Alice wrote three consecutive even numbers. The sum of the three is 252. This means:

`a+(a+2)+(a+4)=252`

The first term is even. Each consecutive even term is two more than the previous term. Simplify:

`3a+6=252\\3a=246\\a=84`

In other words, Alice's first number was 84.

Pat wrote three consecutive odd numbers. His numbers were larger than Alice's numbers. Similar to Alice, we can write:

`(p+1)+(p+3)+(p+5)=x`

The first term is odd. Each consecutive odd term will be 1 more, then 3 more, then 5, etc. We want to find Pat's sum, or x.

We are told that the difference between the largest of Pat's and Alice's numbers is 25. Therefore:

`(p+5)-(a+4)=25`

Simplify. Substitute a. Solve for p:

`p-a+1=25\\p-84=24\\p=108`

Therefore, Pat's sum is:

`(108+1)+(108+3)+(108+5)=333`