Competition · AMC preparation · step 4 of 4
AMC 8 · 2024 · #10
Grade 5 arithmeticPick an answer.
AMC 8 2024 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
This is a rate problem: ppm per year times years gives ppm of increase, which then adds to a starting ppm. Tool #8 (Analyze Units) keeps the recipe honest — "years × (ppm/year) = ppm," and "ppm + ppm = ppm." The only tricky arithmetic is 1.515 × 50, where Tool #9 (Easier Related Problem) lets us replace it with the friendlier 1.5 × 50 = 75 and then add a small correction. Finally, since the question is multiple-choice, Tool #3 (Eliminate Possibilities) confirms the answer against the five choices.
Count the years
Subtract the years: 2030 − 1980 = 50 years — years minus years is years, so that's how long CO₂ has been climbing.
Subtracting four-digit years to find a span of time is the standard multi-digit subtraction skill from Grade 4.
4.NBT.B.4Analyze The UnitsMultiply rate by years
Multiply rate by time: 1.515 × 50. Split as 1.5×50 = 75 plus 0.015×50 = 0.75, giving a total increase of 75.75 ppm.
Multiplying a decimal by a whole number — and breaking the decimal into easier pieces — is exactly the decimal-arithmetic move from Grade 5.
A steady increase of 1.515 ppm each year, kept up for 50 years, adds up to a total increase of 75.75 ppm.
▸ Why?
Adding the same 1.515 ppm rise once for every one of the 50 years is the same as taking 50 equal groups of 1.515 ppm, which is what 1.515 × 50 means.
▸ Why?
The product 1.515 × 50 comes out to 75.75 because we can split 1.515 into 1.5 and 0.015, multiply each piece by 50 to get 75 and 0.75, and recombine them.
Add to the 1980 level
Add the increase onto the 1980 base (ppm + ppm = ppm): 338 + 75.75 = 413.75 ppm, the expected 2030 level.
Adding a whole number and a decimal by lining up the decimal point is a standard Grade 5 decimal-addition skill.
5.NBT.B.7Analyze The UnitsRound and match the choices
The tenths digit 7 rounds up: 413.75 ≈ 414, matching (B); the other choices need a far larger or smaller rate, so eliminate them.
Rounding a decimal to the nearest whole number by looking at the tenths digit is the rounding-decimals skill introduced in Grade 5.
5.NBT.A.4Eliminate PossibilitiesThis AMC 8 problem only needs Grade 5 decimal arithmetic and rounding you already know!
- Count the years
- Multiply rate by years
- Add to the 1980 level
- Round and match the choices
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