Competition · AMC preparation · step 4 of 4
AMC 8 · 2004 · #7
Grade 6 rate-ratioPick an answer.
AMC 8 2004 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The problem hands us a two-step recipe in words: subtract age from 220, then take 80%. Tool #3 (Set Up an Equation) is the cleanest match — translate each English sentence into an arithmetic expression and evaluate in order. No invariant, no pattern, no guessing required. Just two operations and a rounding step.
Find the maximum rate
Subtract the age from 220: the maximum heart rate M is 194.
Naming the maximum with a letter makes the second step easy to write: "80% of M."
6.EE.A.2Eliminate PossibilitiesTake 80 percent
The target is 80% of M: multiply 194 by 0.80 to get 155.2.
"80% of" is the Grade 6 percent move: convert 80% to 0.80, then multiply.
The target heart rate is found by multiplying the maximum heart rate by 0.80, because the target is 80% of the maximum.
▸ Why?
"80% of the maximum" means 80 out of every hundred of the maximum, and a percent of a quantity is exactly (that number over 100) times the quantity — so 80% of the maximum is (80/100) = 0.80 times it.
Round to a whole number
The tenths digit 2 is less than 5, so round 155.2 down to 155.
Standard rounding rule: tenths digit under 5 means keep the whole-number part as-is.
5.NBT.A.4Eliminate PossibilitiesWord-recipe problems become easy once you write each sentence as an expression. Here: 220 - 26 = 194, then 0.80 × 194 = 155.2, then round to 155. Three small steps, no algebra needed.
- Find the maximum rate
- Take 80 percent
- Round to a whole number
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