Competition · AMC preparation · step 4 of 4
AMC 8 · 2008 · #1
Grade 3 arithmeticPick an answer.
AMC 8 2008 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Three things happen in order — food cost, rides cost, money left — and only the food cost is given directly. Tool #7 (Identify Subproblems) breaks the story into three single-step computations so each one stays simple. Tool #3 (Write an Equation) gives us the one short formula we need for each step (multiply for rides, add for total spent, subtract for what's left).
Find the rides cost
Rides cost twice the $12 food, so doubling gives $24.
"Twice" is the Grade 3 "groups of" idea — two groups of 24.
3.OA.A.1Eliminate PossibilitiesAdd the two purchases
Add both purchases: $12 plus $24 gives $36 total spent.
Both costs are now known, so adding them is one straightforward step.
2.NBT.B.5Identify SubproblemsSubtract from the starting money
Subtract the $36 spent from the $50 start to get $14 left.
"How much is left" is always a subtraction — starting amount minus what went away.
The dollars Susan still has equal her starting fifty once the full amount she spent is taken away.
▸ Why?
Her fifty dollars divides with no gap or overlap into the part that was spent and the part still kept, so the spent part and the kept part add back to fifty.
▸ Why?
Since the spent part and the kept part add to fifty, the kept part is found by taking the spent part out of fifty, because subtraction undoes that addition.
▸ Why?
The amount spent is the twelve-dollar food cost joined with the ride cost, and the ride cost is two equal copies of that twelve dollars because "twice as much" means two of it.
▸ Why?
The food cost and the ride cost are separate amounts with no overlap, so putting them together adds them into one spent total.
▸ Why?
"Twice as much" names two equal groups of the food amount, and counting equal groups is multiplication by two.
Three small steps in the right order — double, add, subtract — turn this AMC 8 problem into easy Grade 3 arithmetic.
- Find the rides cost
- Add the two purchases
- Subtract from the starting money
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