The expression 9a + 6s is the cost for a adults and s students to see a musical performance.
a. Find the total cost for three adults and five students.
b. The number of adults and students in a group both double. Does the cost double? Explain your answer using an example.
c. The number of students doubles, but the number of adults is cut in half. Is the cost the same? Explain your answer using an example
a. Substitute 3 for a and 5 for s and compute.
27 + 30 = ___?
b. Does 9*(2a) + 6*(2s) = 2*(9a + 6s) ?
The order that three numbers are multiplied does not affect the result.
c. Does 9*(2a) + 6*(s/2) = (9a + 6s) ?
Put another way, does
18a + 3s = 9a + 6s
Not unless 3a = s
a. 105 for 5 students and 108 for 3 adulots
109
a. To find the total cost for three adults and five students, we can substitute the values into the expression 9a + 6s.
With three adults (a = 3) and five students (s = 5), the expression becomes:
9(3) + 6(5) = 27 + 30 = 57
So, the total cost for three adults and five students is 57.
b. When both the number of adults and students in a group double, we need to determine if the cost also doubles. Let's use an example to understand this:
Let's say initially we had 2 adults (a = 2) and 3 students (s = 3). The expression for the cost would be:
9(2) + 6(3) = 18 + 18 = 36
Now, if the number of adults and students double, we would have 4 adults (a = 4) and 6 students (s = 6). The expression for the cost would be:
9(4) + 6(6) = 36 + 36 = 72
Comparing the initial cost (36) to the new cost (72), we can see that the cost has indeed doubled. So, when the number of adults and students both double, the cost also doubles.
c. When the number of students doubles, but the number of adults is cut in half, we need to determine if the cost remains the same. Let's use an example to understand this:
Let's say initially we had 4 adults (a = 4) and 6 students (s = 6). The expression for the cost would be:
9(4) + 6(6) = 36 + 36 = 72
Now, if the number of students doubles and becomes 12 (s = 12), but the number of adults is halved and becomes 2 (a = 2), the expression for the cost would be:
9(2) + 6(12) = 18 + 72 = 90
Comparing the initial cost (72) to the new cost (90), we can see that the cost is not the same. Therefore, when the number of students doubles and the number of adults is halved, the cost is not the same.