Appearance
question:Bob buys 50 feet of rope. He uses a 5th of it to make a small piece of art. He takes the rest and gives half of it to the friend. After that, he cuts 2-foot sections. How many sections does he get?
answer:Bob buys 50 feet of rope. He uses 1/5 of it, so he uses 50 * 1/5 = 10 feet of rope for the small piece of art. He has 50 - 10 = 40 feet of rope left. He gives half of it to his friend, so he gives 40 * 1/2 = 20 feet of rope to his friend. He has 40 - 20 = 20 feet of rope left for himself. He cuts 2-foot sections, so he can cut 20 / 2 = 10 sections of rope. 10 The answer is: 10
question:During a gymnastics meet, each gymnast shook hands with every gymnast on every team (excluding themselves). Subsequently, a coach only shook hands with the gymnasts on her own team. In total, there were 281 handshakes. Determine the minimum number of handshakes the coach could have been involved in.
answer:Let n be the number of gymnasts on each team. Each gymnast shakes hands with n-1 gymnasts on their own team, so there are n(n-1) handshakes within each team. Since there are n teams, the total number of handshakes within teams is n(n-1)n. The coach only shakes hands with the gymnasts on her own team, so she is involved in n-1 handshakes. Therefore, the total number of handshakes is n(n-1)n + (n-1). We are given that this total is 281, so we can set up the equation n(n-1)n + (n-1) = 281 and solve for n. Expanding and rearranging, we have n^3 - n^2 + n^2 - n + n - 1 = 281. Simplifying, we get n^3 - 1 = 281. Since n is a positive integer, we can take the cube root of both sides to find n = 6. Therefore, the minimum number of handshakes the coach could have been involved in is n-1 = 6-1 = boxed{5}.The answer is: 5
question:takes Polly 20 minutes to cook breakfast every day. She spends 5 minutes cooking lunch. She spends 10 minutes cooking dinner 4 days this week. The rest of the days she spends x minutes cooking dinner. How many minutes does Polly spend cooking this week? If we know the answer to the above question is 305, what is the value of unknown variable x?
answer:Polly spends 20 minutes cooking breakfast every day, so for 7 days in a week, she spends 20 * 7 = 140 minutes cooking breakfast. She spends 5 minutes cooking lunch every day, so for 7 days in a week, she spends 5 * 7 = 35 minutes cooking lunch. She spends 10 minutes cooking dinner 4 days this week, so she spends 10 * 4 = 40 minutes cooking dinner on those days. The remaining days she spends x minutes cooking dinner, so the total time spent cooking dinner on those days is x * (7 - 4) = 3x minutes. The total time Polly spends cooking in a week is the sum of the time spent cooking breakfast, lunch, and dinner: 140 + 35 + 40 + 3x. We are given that the total time spent cooking in a week is 305 minutes, so we can write: 140 + 35 + 40 + 3x = 305. Simplifying the left side, we get: 215 + 3x = 305. Subtracting 215 from both sides, we get: 3x = 90. Dividing both sides by 3, we get: x = 30. The value of x is 30. 30 The answer is: 30
question:f each bird eats 7 berries per day and Samuel has 5 birds, how many berries will Samuel's birds eat in a span of 4 days?
answer:If each bird eats 7 berries per day, then 5 birds will eat 5 * 7 = 35 berries per day. In a span of 4 days, the birds will eat 35 * 4 = 140 berries. 140 The answer is: 140