Study on the flyISEE UpperMathematics AchievementRatios and proportions; distance-rate-time
Mathematics Achievement
Scale, rates and similar figures all belong to Ratios and proportions; distance-rate-time in Mathematics Achievement.
Similar figures follow a key rule: if side lengths are scaled by a factor, area is scaled by the square of that factor, so doubling every side makes the area four times larger, not twice. Work-rate problems are handled by finding the output of one worker or machine per hour, then scaling to the new number and time.
Equal-cost statements set up a proportion between two prices. Distance-rate-time items use distance equals rate times time, and units must agree before any calculation, such as converting minutes to hours.
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Question 1Mid
A triangle has side lengths 6, 8, and 10 and area 24 square units. A second triangle is similar to it, and the side corresponding to the side of length 8 has length 12. What is the area of the second triangle?
Answer: C — 54
The side-length scale factor is . Areas scale by the square of the side-length scale factor, so the area scale factor is . The second triangle’s area is .
Question 2Easier
At a farmers market, seven sacks of rice cost the same as twenty-one sacks of flour. If one sack of flour costs $3, what is the price of one sack of rice?
Answer: B — $9
Twenty-one sacks of flour cost , and that equals the cost of the 7 sacks of rice, so one sack of rice costs . (A) just copies the given flour price, while (C) and (D) apply the wrong sack ratio (treating it as or instead of ).
Question 3Easier
5 identical machines produce 150 parts in 6 hours. At the same per-machine rate, how many parts will 7 machines produce in 6 hours?
Answer: C — 210
Each machine produces parts per hour. Thus 7 machines produce parts.
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