AMC 10 · 2007 · #1
Grade 6 arithmeticPick an answer.
The question compares two people, so Tool #7 (Identify Subproblems) splits it into three clean pieces: what Susan pays, what Pam pays, and the difference between them. Inside each piece the work is the same shape — full-price total, then apply that buyer's percent discount. Tool #8 (Analyze the Units) keeps every number in dollars so the discount is taken on a dollar total and the final subtraction compares dollars to dollars.
Full-price cost for each buyer
The full prices come to 80 and 100.
Same price on every ticket, so total cost is just price times number of tickets.
4.OA.A.3Identify SubproblemsApply Susan's 25% discount
The first discount leaves 60.
Percent means per hundred, so 25% off a total is a quarter of that total taken away.
Taking twenty-five percent off a total is taking away a quarter of it.
▸ Why?
A percent is a count out of every hundred, so twenty-five out of a hundred is one part in four.
▸ Why?
A quarter is one of four equal shares, so removing it leaves the other three shares.
Apply Pam's 30% discount
The second, larger discount still leaves 70.
A percent of 100 is that many dollars, because a percent is already a count per hundred.
6.RP.A.3Identify SubproblemsCompare the two totals
Comparing gives 10, choice (C).
"How much more" is a subtraction of the two final amounts.
4.OA.A.3Identify SubproblemsFind each person's full-price total first, take their percent off, then subtract the two final prices to compare.
- Full-price cost for each buyer
- Apply Susan's 25% discount
- Apply Pam's 30% discount
- Compare the two totals