# TFS Math Corner: Weekly Problems From the LFHS Math Department

The 2nd period Advanced Mathematics Problem Solving (AMPS) class of 2017-2018 is challenging any Lake Forest High School student to solve any of the following three problems of varying difficulty. There are three categories of problems and they are labeled as they appear: Easy, Moderate, and Hard. New problems will be published every two weeks.

We will also be publishing a Weekly Math problem. The Weekly Math Problem will vary in difficulty from week to week. A new problem will be released every Friday.

Try as best as you can to solve any of the following problems and when you do, please submit your solution(s) AND WORK to the Google Form link posted below.

http://bit.ly/2fmoJQH

Win LFHS Prizes!

### Weekly problem

There are two integers under the conditions:

1) The larger integer is 5/2 times the smaller.

2) If twice the smaller is subtracted from twice the larger, the difference is 12.

Find the two integers.

Solution posted on: 9/29

### “Easy” problem

Find the equation of a line that crosses the point (3,5) and is perpendicular to the line

y-1=12(x-2)

Solution posted on: 10/6

### “Moderate” problem

Imagine a circular pizza. One person cuts it in half, then cuts the half piece in half and so on. Each time he cuts the piece in half, he labels it with the letters of the alphabet – the first being labeled as A, the next half cut as B. If the radius of the pizza is 6.383 inches, what is the sum of the areas of pieces H and K?

(Round Area to nearest whole number)

Solution posted on: 10/6

### “Hard” problem

Problem: a, b, c, d and e are distinct integers. If

(8-a)(8-b)(8-c)(8-d)(8-e)=63

Find the product of each of the integers.

Solution posted on: 10/6

You will be informed on whether or not you submitted a correct response for any of the problems via your school email.

If you submit the correct solution (with work shown) to the Easy, Moderate, and/or Hard problems, you will be entered into a raffle where you can win extra credit from your math teacher! (amount of extra credit will vary from math teacher to math teacher). One winner from each level will be drawn.

If you submit the correct solution to the Weekly Problem, you will be entered into a semester-long raffle. Raffle prizes can include gift cards, LFHS booster attire, and possibly free tickets to dances.

Try your best and good luck “math’in”!