question in description

Question

Mr. Newman bought 8 tickets to a chili supper

and spent a total of $30. He bought a combination

of adult tickets for $5 each and child tickets $3 each.

Which system of equations below will determine the

number of child tickets, c, and the number of adult

tickets, a, he bought?

A) 8a + 5c = 30 B) a + c = 8

a + c = 3 3a + 5c = 30

C) 5a + 3c = 8 D) 5a + 3c = 30

a + c = 30 a + c = 8

E) None of the above

Answer 1

Let,

a = the number of adult tickets

c = the number of child tickets

Mr. Newman bought 8 tickets in total, so the number of adult tickets plus the number of child tickets adds up to 8 tickets total. That means,

a + c = 8

Adult tickets are $5 each, so Mr. Newman would spend $5 for each of the number of adult tickets he bought. That means he would spend 5a on adult tickets.

Child tickets are $3 each, so Mr. Newman would spend $3 for each of the number of child tickets he bought. That means he would spend 3c on child tickets.

He spends $30 total. So, when we think about it, he spends 5a + 3c in total. That means,

5a + 3c = 30

So, our two equations are:

5a + 3c = 30

a + c = 8

Answer 2

Hi Sal N.

Choice D

You want to align your variables with correct totals.

You have two totals

8 = Total number of tickets purchased

$30 = Total cost

You have two prices

Adult tickets cost $5 each

Child tickets cost $3 each

You are also given variables

a = represents adult ticket

c = represents child ticket

You know there was a combination of adult and child tickets purchased. The following equations are needed: an equation that represents the total number of tickets and an equation for the total cost of the tickets for the combinations

a + c = 8

5a + 3c = 30

You can use substitution or elimination to solve for the variables then check your numbers in the original equations to see if they are correct. You can also graph your system of equations.