Answer:
333
Step-by-step 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:
[tex]a+(a+2)+(a+4)=252[/tex]
The first term is even. Each consecutive even term is two more than the previous term. Simplify:
[tex]3a+6=252\\3a=246\\a=84[/tex]
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:
[tex](p+1)+(p+3)+(p+5)=x[/tex]
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:
[tex](p+5)-(a+4)=25[/tex]
Simplify. Substitute a. Solve for p:
[tex]p-a+1=25\\p-84=24\\p=108[/tex]
Therefore, Pat's sum is:
[tex](108+1)+(108+3)+(108+5)=333[/tex]
