MIT

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question:Bingley has 5 bracelets. Kelly gives Bingley a fourth of her 16 bracelets. Then Bingley gives a third of his bracelets to his little sister. How many bracelets does Bingley have remaining?

answer:Kelly gives Bingley 16/4 = 4 bracelets Bingley now has 5 + 4 = 9 bracelets Bingley gives 9/3 = 3 bracelets to his little sister Bingley now has 9 - 3 = 6 bracelets remaining 6 The answer is: 6

question:Tina buys 3 12-packs of soda for a party. Including Tina, 6 people are at the party. Half of the people at the party have 3 sodas each, 2 of the people have 4 and 1 person has 5. How many sodas are left over when the party is over?

answer:Tina buys 3 12-packs of soda, so she has a total of 3 * 12 = 36 sodas. Including Tina, there are 6 people at the party. Half of the people have 3 sodas each, so 6/2 = 3 people have 3 sodas each. 3 people * 3 sodas each = 9 sodas for these people. 2 people have 4 sodas each, so 2 people * 4 sodas each = 8 sodas for these people. 1 person has 5 sodas. So in total, the people at the party have 9 + 8 + 5 = 22 sodas. Tina started with 36 sodas and the people at the party consumed 22 sodas, so 36 - 22 = 14 sodas are left over when the party is over. 14 The answer is: 14

question:Let a bowtie b = a+sqrt{b+sqrt{b+sqrt{b+...}}}. If 4bowtie y = 10, find the value of y.

answer:We have 4bowtie y = 4+sqrt{y+sqrt{y+sqrt{y+...}}} = 10. Subtracting 4 from both sides, we have sqrt{y+sqrt{y+sqrt{y+...}}} = 6. Squaring both sides, we have y+sqrt{y+sqrt{y+...}} = 36. Substituting sqrt{y+sqrt{y+sqrt{y+...}}} with 6, we have y+6=36. Subtracting 6 from both sides, we have y = boxed{30}. The answer is: 30

question:Ellen is painting flowers on a vase. It takes her 5 minutes to paint a lily, 7 minutes to paint a rose, 3 minutes to paint an orchid, and x minutes to paint a vine. How long will it take her to paint 17 lilies, 10 roses, 6 orchids and 20 vines? If we know the answer to the above question is 213, what is the value of unknown variable x?

answer:It takes Ellen 5 minutes to paint a lily, so it will take her 5 * 17 = 85 minutes to paint 17 lilies. It takes her 7 minutes to paint a rose, so it will take her 7 * 10 = 70 minutes to paint 10 roses. It takes her 3 minutes to paint an orchid, so it will take her 3 * 6 = 18 minutes to paint 6 orchids. It takes her x minutes to paint a vine, so it will take her x * 20 minutes to paint 20 vines. The total time it will take her to paint everything is the sum of the times for each type of flower: 85 + 70 + 18 + x * 20. We are given that the total time is 213 minutes, so we can write: 85 + 70 + 18 + x * 20 = 213. Simplifying the left side, we get: 173 + x * 20 = 213. Subtracting 173 from both sides, we get: x * 20 = 40. Dividing both sides by 20, we get: x = 2. The value of x is 2. 2 The answer is: 2