AMC 10 · 2009 · #3
Grade 7 rate-ratioPick an answer.
The sentence hands you the finished value on the left and asks for the starting number on the right, so the natural move is to compute the left side, then undo the 'one-third more' step to walk back to the original number.
Compute twenty percent less than 60
The first sentence gives a plain value.
'Percent less' means slice that share off the whole, not add it on.
7.RP.A.3Identify SubproblemsWrite 'one-third more than n'
The second writes it as a multiple of the hidden number.
'One-third more' scales the number up to 4/3 of itself, not just to a third of it.
One third more scales a number up to four thirds of itself, not merely to a third of it.
▸ Why?
The result is the original plus an extra piece, so both parts have to be counted.
▸ Why?
That extra piece is one of three equal shares of the original, so it is a third of it and no more.
Undo the scaling to find n
Undoing that multiplication gives 36, choice (B).
To find the original from a scaled-up value, divide by the same factor you multiplied by.
6.EE.B.7Work Backwards'One-third more' means times four-thirds, so to go back you divide by four-thirds.
- Compute twenty percent less than 60
- Write 'one-third more than n'
- Undo the scaling to find n