SCIENCE CENTER The expression 20a + 13c is the cost (in dollars) for a adults and c students to enter a science center. A. How much does it cost for an adult? A student? Explain your reasoning. b. Find the total cost for 4 adults and 24 students. c. You fi nd the cost for a group. Then the numbers of adults and students in the group both double. Does the cost double? Explain your answer using an example.

 A. The expression to find the cost for adults and students to enter a science center is 20a + 13c, where 'a' represents the number of adults and 'c' represents the number of students.

To find the cost for one adult, you can simply substitute a = 1 into the expression because it means we are considering just one adult. Doing so, we get:

20 * 1 + 13 * 0 = 20 + 0 = $20

Hence, it costs $20 for one adult.

Similarly, to find the cost for one student, substitute c = 1 into the expression and keep the number of adults as 0 because we are only considering the cost for one student:

20 * 0 + 13 * 1 = 0 + 13 = $13

Therefore, it costs $13 for one student.

B. To find the total cost for 4 adults and 24 students, substitute a = 4 and c = 24 into the expression:

20 * 4 + 13 * 24 = 80 + 312 = $392

So, the total cost for 4 adults and 24 students is $392.

C. If you double the number of adults and students, the expression to find the new cost would be 20(2a) + 13(2c). Let's use a specific example to illustrate if the cost doubles:

Suppose we have 1 adult and 1 student, the original cost would be:

20 * 1 + 13 * 1 = $20 + $13 = $33

Now let's double the number of both adults and students. So we have 2 adults and 2 students. The new cost would be:

20 * 2 + 13 * 2 = $40 + $26 = $66

As you can see, the new cost ($66) is exactly double the original cost ($33). This will be true regardless of the number of adults and students because when you double both 'a' and 'c' in the expression, you are effectively taking 2 out as a common factor, which doubles the entire expression, hence doubling the total cost.