AMC 8 · 2009 · #23
Grade 4 algebraPick an answer.
AMC 8 2009 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Each answer choice is a total like 28. Once we know the total T, the "boys - girls = 2" condition pins down the split exactly: girls = , boys = . So Tool #6 (Guess and Check) lets us try each choice and see which one makes (boys)² + (girls)² equal 394. Tool #2 (Make a Systematic List) keeps the five trials organized in a clean table so we don't lose track. This avoids setting up a quadratic equation — we just test five small cases.
Subtract the 6 left over from the 400 she brought: 394 jelly beans were handed out.
Subtracting the leftover from the starting amount gives the amount used — the standard "start, change, result" word-problem move.
4.OA.A.3Guess And CheckFor any total T, the two-more-boys rule splits it: girls get and boys get .
If two numbers differ by 2 and add to T, the smaller one is the average minus 1 and the larger is the average plus 1 — a Grade 4 word-problem habit.
4.OA.A.3Make A Systematic ListFor each answer choice, compute girls, boys, and girls² + boys², then compare each sum to 394.
Squaring small two-digit numbers (12², 13², …, 18²) uses the multiplication fluency built in Grade 3.
3.OA.C.7Make A Systematic ListOnly T = 28 makes the sum exactly 394; values jump 340 → 394 → 452, so the match is unique.
Adding two three-digit numbers and matching the target is the Grade 4 multi-digit addition standard, used here as the "check" step of Guess and Check.
4.NBT.B.4Guess And CheckThe winning row's total, T = 28, is the answer — choice (B), 13 girls and 15 boys.
After Guess and Check confirms one row, that row's total is the answer — the closing move of Tool #6.
4.OA.A.3Guess And CheckYou don't need a quadratic equation — with five answer choices and the "2 more boys than girls" rule, Guess and Check with Grade 4 arithmetic finds the answer in one tidy table!