Competition · AMC preparation · step 4 of 4
AMC 10 · 2020A · #4
Grade 6 rate-ratioPick an answer.
AMC 10 2020 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Tool #8 (Analyze the Units) is perfect — the question is built entirely from rates (mile/hour, mile/gallon, /mile, /gallon, /hour). Track units through and the formula writes itself. Tool #7 (Subproblems) splits the work into earnings rate, gas-cost rate, and net rate — all per hour, so we don't even need the total 120 miles. Tool #3 (Eliminate) checks the magnitude: gross is 0.50/mi = $30/hr), so the net must be a bit less than 30 — answers ≤ 20 are out.
Find the pay per hour
Gross pay: speed times pay-per-mile cancels the miles, leaving $30 per hour.
Speed × pay-per-mile gives pay-per-hour because miles cancel.
6.RP.A.3Analyze The UnitsFind the gas cost per hour
Gas cost: each hour's 60 miles burns 2 gallons, costing $4 per hour.
Chain three rates so miles and gallons both cancel — left with dollars per hour.
Chaining the rates so the shared units cancel leaves exactly the unit you want.
▸ Why?
Each rate is quoted per one fixed unit, so it can be multiplied by a count of those units.
▸ Why?
At a steady rate the amount is that rate times the count, so the chain of rates behaves like one.
Subtract gas from pay
Net pay: gross minus gas, $30 - $4 = $26 per hour, which is choice (E).
Earnings minus the only expense leaves net pay.
4.OA.A.3Identify SubproblemsSanity-check the size
Sanity check: gross is $30 per hour and gas only $4, so net lands at $26 — no smaller choice fits.
Net = gross minus expense; only one choice fits the right gap.
6.RP.A.3Eliminate PossibilitiesThis AMC 10 problem only needs Grade 6 "ratios and rates" you already know — earnings $30/hr, gas $4/hr, net $26/hr.
- Find the pay per hour
- Find the gas cost per hour
- Subtract gas from pay
- Sanity-check the size
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