AMC 8 · 2020 · #2

Grade 3 arithmetic

Archetype Arithmetic Expression Decomposition └ Sub-archetype Linear Rate Accumulation

mean-median-mode-rangemulti-digit-arithmetic identify-subproblems ↑ Prerequisites: multi-digit-arithmetic

📏 Short solution 💡 2 insights

Problem

Four friends did yardwork and earned

15,

20,

25, and

40. They want to pool everything and end up with equal amounts. How much money does the friend who earned $40 hand over to the rest of the group?

Pick an answer.

(A)

(B)

$10

(C)

$15

(D)

$20

(E)

$25

AMC 8 2020 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Identify Subproblems

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.

1STEP 1

Add the four earnings to see the whole pile: $100 total to share.

15 +

20 +

25 +

40 = $100

2STEP 2

"Split equally among four" means divide the total by 4 — each fair share is $25.

100 ÷ 4 =

25 per friend

3STEP 3

He starts at $40 but should keep only the$ 25 share, so he hands over $15.

40 -

25 = $15 → (C)

4STEP 4

Check the choices: only $15</span></span> leaves the$ 40 friend with exactly the $25 fair share.

40 -

15 = $25 ✓

Answer

$15

Quick sanity check: the four amounts

15,

20,

25,

40 are not too different, so the fair share

25 should sit roughly in the middle — which it does. The two friends below

25 (

15 and

20) together need

10 +

5 =

15 to reach

25, and the friend at exactly

25 needs nothing. So the

40 friend must supply exactly $15 — matching our answer (C). The books balance, which is exactly what "split equally" requires.

💡Key takeaway

This AMC 8 problem only needs Grade 3 add-subtract and "share equally" division that you already know!

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