Question

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.

Answer 1

Answer:

Step-by-step explanation:

A.  It costs $20 per adult.  If this is a cost fuction, which it is because the wording is "the cost (in dollars) for a adults and c students", adult is a, the cost for 1 adult, 1a, is 20.  That relates the number of adults to the cost of 1 adult.

It costs $13 per student.  Again, this is a cost function, so since student is c, the cost for 1 student, 1c, is 13.  That relates the number of students to the cost of 1 student.

B.  The total cost for 4 adult and 24 students looks like this:

20(4) + 13(24) which is 80 + 312 = $392

C.  If you have 3 adults and 3 students in your group, the cost is 20(3) + 13(3) which is $99.  If you double the number of each, let's see if the cost doubles.  We will "up" the numbers to 6 each.  20(6) + 13(6) = $198.  Is $198 the double of $99.  Yes it is.  Let's do it again to check.  Let's double the 6.

20(12) + 13(12) = $396, and $198 doubled does in fact equal $396. So there you go!

Answer 2

Following are the solution to the given points:

For point a:

• Each adult pays $\ 20$. Whether this is a cost function.
• Because the wording says "the cost (in dollars) for just adults and c students," a person is a, and the cost for one adult, 1a, is 20.
• It is a ratio of the number of people to the cost of one adult.
• Every pupil gets charged $13. Because pupil is c, the cost for one pupil, 1c, is 13.
• This relates the overall number of students to the cost of one pupil.

For point b:

When the Total cost $= 20a + 13c$

Where

$\text{a = adult}\\\\\text{c = student}$

Calculating the total cost for 4 adults and 24 students

$\to a = 4 \\\\ \to c = 24$

$\to 20(4) + 13(24)\\\\\to 80 + 312\\\\\to 392$

For point c:

• When your party consists of three adults and three students, the overall cost is$\ 99 =(20 (3) + 13 (3)).$
• Let's see if the price doubles if you double the amount of each.
• We'll "increase" the number to six for each one of us. $\ 198$ is the sum of $20(6) + 13(6).$ $\ 198$ precisely the same as $\ 99$. That's correct.
• Let's go through it again for good measure.
• Let's double the 6 by two. $\ 20(12) + 13(12) = \ 396$, and $\ 198$ multiplied by two equals $\ 396$.
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