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If Kelly buys t pens priced at 2 dollars each and u pens priced at 4 dollars each, which of the following expresses, in terms of t and u, the average (arithmetic mean) price, in dollars, of these pens?
(A) (3 times t) + (3 times u) over (t + u)
(B) (3 times t) + (3 times u) over (t imes u)
(C) (3 times t times u) over (t + u)
(D) ((2 times t) + (4 times u)) over (t + u)
(E) ((2 times t) + (4 times u)) over (t times u)
解释：
The average price of the pens is equal to the total price of all of the pens divided by the total number of pens.
The average price of the pens is equal to the total price of all of the pens divided by the total number of pens. There are t pens priced at 2 dollars each, so the total price of these pens is 2 times t dollars. There are u pens priced at 4 dollars each, so the total price of these pens is 4 times u dollars. Thus the total price of all of the pens is (2 times t) + (4 times u) dollars, and the total number of pens is t + u, the average price, in dollars, of all of these pens is ((2 times t) + (4 times u)) over (t + u).
正确答案是D。
For every 10 dollars Ken earns mowing lawns, he gives 3 dollars to his younger brother, Tim, who helps him. Which of the following gives the relationship between d, the number of dollars Ken earns, and t, the number of dollars he gives to Tim?
(A) d=(3 times t) over 10
(B) d=(10 times t) over 3
(C) d=3 over (10 times t)
(D) d=10 over (3 times t)
(E) d=(3 times t) minus 10
解释：
For every 10 dollars Ken earns, he gives 3 dollars to Tim. Thus if Ken earns d dollars and gives Tim t dollars, the proportion 10 over 3 equals d over t holds.
For every 10 dollars Ken earns, he gives 3 dollars to Tim. Thus if Ken earns d dollars and gives Tim t dollars, the proportion d over t equals 10 over 3 holds. Multiplying both sides of this proportion by t gives d equals (10 times t) over 3.
正确答案是B。
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