Diana’s favourite coin is a dime. She has a whole bunch of them – she does not know exactly
how many, but she is sure that she has fewer than 250. One day she was arranging them on her
desk in different ways. She found the following:
• When she put them in piles of three, there was 1 dime left over.
• When she put them in piles of four, there was 1 dime left over.
• When she put them in piles of five, there was none left over.
How many dimes does Diana have? Is there only one possible answer?
2007-09-09 15:59:52 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The answer is 1 plus a multiple of both 3 and 4, and also a multiple of 5.
4 possible answers
25 dimes
85 dimes
145 dimes
205 dimes
2007-09-09 16:11:11 · answer #1 · answered by Jonathan S 2 · 0⤊ 0⤋
This boils down to defining the amount in terms of where remainders occur in the numbers tables.
Since you have piles of 5 with no leftovers, but a leftover of 1 with piles of 4, the units digit is 5.
But if the units digit is 5, for the piles of 4 to have 1 leftover, the amount xy5-1 has to be divisible by 4. So this would give us numbers like 45, 65, 85, etc (note the number of tens is an even number). To have piles of 3 with one leftover, the amount xy5-1 has to be divisible by 3, or that the number xy5+5 is divisible by 3. The set of these that intersect the set of numbers for the 3 pile include 84, 144, 204.
2007-09-09 16:14:55 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋
there are multiple answers...
25
85
145
205
2007-09-09 16:08:19 · answer #3 · answered by upernuper 1 · 0⤊ 0⤋