AMC 10 · 2004 · #3
Grade 6 arithmeticPick an answer.
AMC 10 2004 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The whole problem turns on units (Tool #8): the wage is given in dollars but the answer is wanted in cents, and the tax rate is a percent. If you convert the wage to cents first and then take the percent, the answer comes out in cents directly. The trap is to compute 1.45% of 0.29, forgetting to turn dollars into cents — that lands on choice (C). Tool #3 (Eliminate Possibilities) helps because every choice is the same digits 29 shifted by a power of ten, so only the correct unit handling picks the right one.
Convert the wage to cents
The answer is wanted in cents, so convert first: 1 dollar is 100 cents, so 20 dollars is 2000 cents.
Match your units to the question first, so the final number is already in the units you were asked for.
4.MD.A.1Analyze The UnitsTake 1.45% of the wage
A percent is a rate per hundred, so 1.45% of 2000 cents is 0.0145×2000 = 29 cents each hour.
Percent means "out of a hundred", so a percent of a quantity is that many hundredths of it.
A percent of a quantity is that many hundredths of it.
▸ Why?
A percent is a count out of every hundred, so the base decides what one percent is worth.
▸ Why?
A dollar is a fixed bundle of cents, so converting first keeps every quantity in one unit.
Match to a choice and rule out the trap
That is choice (E); the other choices are the same digits shifted by a power of ten — the mark of a dollars-versus-cents slip.
When the choices are the same digits at different decimal places, getting the units right is the whole problem.
4.MD.A.1Eliminate PossibilitiesConvert to the units the question asks for first, then take the percent — here that turns 20 dollars into 2000 cents, and 1.45% of 2000 is 29 cents.
- Convert the wage to cents
- Take 1.45% of the wage
- Match to a choice and rule out the trap