AMC 10 · 2010 · #1
Grade 6 rate-ratioPick an answer.
The question stacks a few small tasks: find the second meeting's length, add the two meetings, express the day in the same unit, then turn the ratio into a percent. Tool #7 (Identify Subproblems) keeps each step clean. Tool #8 (Analyze the Units) is the guardrail: the day is in hours and the meetings in minutes, so the one real trap is comparing them before matching units. Convert the day to minutes and the percent falls out.
Find the second meeting's length
The second meeting runs 90 minutes.
"Twice as long" just means double it, so the second meeting is two of the first stacked together.
4.OA.A.1Identify SubproblemsAdd the two meetings
Together they take 135 minutes.
Total time in meetings is simply the first plus the second, added up.
4.NBT.B.4Identify SubproblemsTurn the whole day into minutes
The whole day is 540 minutes.
You can only compare minutes to minutes, so trade the hours in for the minutes they are worth.
5.MD.A.1Analyze The UnitsDivide and read the percent
Dividing gives 25 percent, choice (C).
Percent is just the part-over-whole fraction rewritten as a piece of 100, and a quarter of anything is 25%.
A percent is the part over the whole rewritten as a piece of a hundred.
▸ Why?
A percent is a count out of every hundred, so any fraction becomes one by rescaling its bottom to a hundred.
▸ Why?
The part is one share of the whole day, and a fraction is exactly that kind of share.
Before you compare two amounts, make sure they are in the same unit — then the percent is just part over whole.