Problem 15 · 2014 Math Kangaroo
Medium
Arithmetic & Operations
casework
Hubert the rabbit loves cabbages and carrots. In one day he eats either 9 carrots, or 2 cabbages, or one cabbage and 4 carrots. In one week Hubert ate 30 carrots. How many cabbages did he eat during this week?
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Answer: B — 7
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Hint 1 of 3
There are 7 days in a week, so Hubert eats one of his three menus on each of the 7 days.
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Hint 2 of 3
Only two of the menus give carrots: the 9-carrot day and the 1-cabbage-and-4-carrots day.
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Hint 3 of 3
Try a few of each carrot-day until the carrots add up to 30, then count cabbages on every day.
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Approach: find which days give the 30 carrots, then count cabbages
- Only two kinds of day give carrots: a 9-carrot day, or a day of 1 cabbage and 4 carrots.
- Two 9-carrot days give 18 carrots, and three of the ‘1 cabbage + 4 carrots’ days give 12 more — that is 18 + 12 = 30 carrots, using 5 days.
- Those three mixed days give 3 cabbages, and the 2 days left over are 2-cabbage days, giving 2 × 2 = 4 more.
- Total cabbages = 3 + 4 = 7.
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