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Basic Mathematics

Ratio, Rate, and Proportion

Direct Variation


A worker can harvest all the corn in 9 m29 \text{ m}^2 of farmland in 1/31/3 hours. How many hours will the worker need to harvest all the corn in 432 m2432 \text{ m}^2 of farmland?

Gift set A contains 88 red golf balls and 22 white golf balls, and gift set B contains 55 green golf balls and 33 white golf balls. Suppose that Tom has some gift sets A and Judy has some gift sets B, and that each person has the same number of golf balls. Then what is the fraction of white balls among all the golf balls the two persons have?

Two right triangles ABCABC and DEFDEF in the above figure are similar, where the corresponding side of AB\overline{AB} is EF.\overline{EF}. If AC=3,\lvert{\overline{AC}}\rvert=3, AB=4\lvert{\overline{AB}}\rvert=4 and DE=l=18,\lvert{\overline{DE}}\rvert=l=18, what is the length of EF?\overline{EF}?

The value of yy changes directly proportional to the value of x.x. If y=18y=18 when x=6,x=6, what is the value of yy when x=29.5?x=29.5 ?

The value of yy varies directly with the square of x.x. If y=22y=22 when x=11,x=11, what is the value of yy when x=22?x=22 ?


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