Competition · AMC preparation · step 4 of 4
AMC 8 · 2020 · #2
Grade 3 arithmeticPick an answer.
AMC 8 2020 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The question hides three smaller, easier questions inside it: (1) what is the total pile of money? (2) what is each friend's fair share? (3) how much more than the fair share did the $40 friend start with? Tool #7 (Identify Subproblems) is perfect because solving these three pieces in order turns a one-line word problem into three single-step arithmetic problems we can already do. Tool #3 (Eliminate Possibilities) is held in reserve: once we have an answer, we can confirm it against the five multiple-choice options to make sure no arithmetic slip occurred.
Add the four amounts
Add the four earnings to see the whole pile: $100 total to share.
Adding four whole-dollar amounts that are all under $50 is a Grade 3 "add within 1000" calculation.
3.NBT.A.2Identify SubproblemsDivide into equal shares
"Split equally among four" means divide the total by 4 — each fair share is $25.
"Share equally among four" is the Grade 3 fair-share division word-problem move.
3.OA.A.3Identify SubproblemsFind the extra to give away
He starts at $40 but should keep only the $25 share, so he hands over $15.
Subtracting 25 from 40 is a Grade 3 single-step subtraction within 100.
The friend who earned $40 hands over exactly the difference between the $40 he earned and each friend's $25 equal share.
▸ Why?
To finish level with everyone else he must be left holding only the equal share, so whatever sits above that share is exactly the money that leaves his hands.
▸ Why?
His $40 pile is made of two parts with nothing lost — the money he keeps and the money he gives away — so keep plus give equals $40.
▸ Why?
He keeps the $25 share, so the money he gives is found by peeling that back out, $40 - $25, which is subtraction undoing the keep-plus-give addition.
▸ Why?
Each friend's equal share is $25 because the pooled $100 is shared into four piles of the same size, and one such pile is $100 ÷ 4.
▸ Why?
The pooled $100 is four equal shares put back together, so $100 is four equal groups of one share.
▸ Why?
One share is then recovered from $100 by dividing by four, since division reverses the making of equal groups.
Verify the result
Check the choices: only $15 leaves the $40 friend with exactly the $25 fair share.
Plugging each choice back and subtracting from $40 is still Grade 3 subtraction — perfect for a quick double-check.
3.NBT.A.2Eliminate PossibilitiesThis AMC 8 problem only needs Grade 3 add-subtract and "share equally" division that you already know!
- Add the four amounts
- Divide into equal shares
- Find the extra to give away
- Verify the result
A parent dashboard for the family lives at sensimlab.com.