Question

HELP! URGENT!

Answer 1

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:

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

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:

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