AMC 8 · 2009 · #2
Grade 6 rate-ratioPick an answer.
AMC 8 2009 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The phrase "for every 4 sports cars, 7 sedans" sets up a repeating pattern: (4, 7), (8, 14), (12, 21), … — each step adds one more 4 : 7 group. Tool #5 (Look for a Pattern) makes that ladder visible and shows that the sports-car column is multiplied by some whole number to reach 28, so the sedan column gets multiplied by the same number. Tool #6 (Guess and Check) is the natural backup: test each answer choice against the 4 : 7 ratio and keep the one that matches.
List the ratio as a table — each row is one 4 : 7 group, and each new group adds 4 sports cars and 7 sedans.
Listing a few rows turns the abstract ratio into something you can literally count up.
6.RP.A.3Look For A PatternFind the scaling factor: 28 ÷ 4 = 7, so 28 sports cars is 7 groups of 4 : 7.
The number of groups is the same for both columns — that is what "constant ratio" means.
6.RP.A.3Look For A PatternScale the sedan side the same way: 7 groups × 7 sedans each = 49 → (D).
Scaling both parts of a ratio by the same whole number keeps the ratio equivalent.
5.NF.B.5Look For A PatternWhen two quantities grow at a constant ratio, find how many times one side is scaled up — then scale the other side by the same number.