On each of the first three days of the month, Danny ate twice the number of apples he had eaten the day before. The ratio of the number of apples he ate on the third day to the number he ate on the fourth day is \(\dfrac35.\) What is the ratio of the number of apples Danny ate on the second day of the month to the number he ate on the fourth day?
A) \(\dfrac3{10}\)
B) \(\dfrac3{20}\)
C) \(\dfrac12\)
D) \(\dfrac65\)
E) \(\dfrac{10}3\)
Answer: A
Source: Economist
On each of the first three days of the month, Danny ate twice the number of apples he had eaten the day before. The rati
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Let X equal the number of apples eaten on the first day.
So the second day he ate 2X apples and the third day 4X.
Let the number of apples he ate on the 4th day equal Y.
The ratio of the number of apples eaten on the third day to the number eaten on the 4th day is then:
4X/Y = 3/5
Y is then equal to:
20X/3
So the ratio of the number of apples eaten on the second day to the number eaten on the 4th day is:
2X/Y = 2X/(20X/3) = [spoiler]3/10, A[/spoiler]
So the second day he ate 2X apples and the third day 4X.
Let the number of apples he ate on the 4th day equal Y.
The ratio of the number of apples eaten on the third day to the number eaten on the 4th day is then:
4X/Y = 3/5
Y is then equal to:
20X/3
So the ratio of the number of apples eaten on the second day to the number eaten on the 4th day is:
2X/Y = 2X/(20X/3) = [spoiler]3/10, A[/spoiler]