Last year, Hunter's history and math classes had regular tests. Each history test had 2 questions and each math test had 7 questions. If Hunter had to answer the same number of history questions and math questions last year, what is the smallest number of each type of question he must have answered?
[___] questions
Let's assume that Hunter answered x questions for both history and math last year.
Since each history test had 2 questions, the total number of history questions answered by Hunter is 2x.
Since each math test had 7 questions, the total number of math questions answered by Hunter is 7x.
To find the smallest number of each type of question he must have answered, we need to find the smallest value of x that satisfies the equation:
2x = 7x
Let's divide both sides of the equation by x:
2 = 7
Since 2 is not equal to 7, this equation cannot be satisfied.
Therefore, it is not possible for Hunter to have answered the same number of history questions and math questions last year.
Last year, Hunter's history and math classes had regular tests. Each history test had 2 questions and each math test had 7 questions. If Hunter had to answer the same number of history questions and math questions last year, what is the smallest number of each type of question he must have answered?
[blank] questions
Apologies for the confusion earlier. Let's reconsider the problem.
To find the smallest number of each type of question that Hunter must have answered, we need to determine the least common multiple (LCM) of 2 and 7.
The prime factorization of 2 is 2, and the prime factorization of 7 is 7. The LCM is found by taking the highest power of each prime factor that appears in either number. In this case, the LCM is simply (2 * 7) = 14.
Therefore, Hunter must have answered a minimum of 14 questions in total, with an equal number of history and math questions.
So the answer is:
[14] questions
Brian has 45 forks and 42 knives to place in silverware holders at the fast food restaurant where he works. He wants to distribute them equally, with no forks or knives left over. What is the greatest number of silverware holders Brian can stock?
[blank] silverware holders
To find the greatest number of silverware holders Brian can stock, we need to determine the greatest common divisor (GCD) of 45 and 42.
The prime factorization of 45 is 3 * 3 * 5 = 3^2 * 5.
The prime factorization of 42 is 2 * 3 * 7.
To find the GCD, we take the lowest power of each prime factor that appears in both numbers. In this case, the GCD is 3.
Therefore, Brian can stock a maximum of 3 silverware holders, each containing an equal number of forks and knives.
So the answer is:
[3] silverware holders
Adriana owns a business and assigns two of her employees their shifts. She assigns the first employee shifts in blocks of 2 hours, and she assigns the second worker shifts in blocks of 10 hours. If both workers must receive the same number of hours, what is the minimum number of hours each must be assigned?
[blank] hours
To find the minimum number of hours each worker must be assigned, we need to find the least common multiple (LCM) of 2 and 10.
The prime factorization of 2 is 2, and the prime factorization of 10 is 2 * 5.
The LCM is found by taking the highest power of each prime factor that appears in either number. In this case, the LCM is (2 * 5) = 10.
Therefore, the minimum number of hours each worker must be assigned is 10 hours.
So the answer is:
[10] hours.
Layla watered all the flowers at a business park. While watering, she noticed the daisies had been planted in groups of 11 and the lilies had been planted in groups of 3. If Layla watered the same number of each flower, what is the minimum number of each that she must have watered?
[__] flowers
To find the minimum number of daisies and lilies that Layla must have watered, we need to find the least common multiple (LCM) of 11 and 3.
The prime factorization of 11 is 11, and the prime factorization of 3 is 3.
The LCM is found by taking the highest power of each prime factor that appears in either number. In this case, the LCM is 11 * 3 = 33.
Therefore, the minimum number of daisies and lilies that Layla must have watered is 33 flowers.
So the answer is:
[33] flowers.
At a concert, the band has 14 men's T-shirts and 28 women's T-shirts. The band wants to set up tables to sell the shirts, with an equal number of men's and women's shirts available at each table and no shirts left over. What is the greatest number of tables the band can sell shirts from?
[___] tables