Defining your variables , writing answer in sentence

Question

the bronx zoo charges an admission fee of $14 for adults and $11 for children one july day a total of $11490 was collected from 960 admissionS. how many children and adults were admtied   ?? 

Answer 1

Since we have adults and children, why don't we define our variables as 'a' and 'c' respectively?

Here's what we know:

14a + 11c = 11490 (the total revenue from ticket costs are 11490)

a + c = 960 (960 tickets were sold in total)

 

We can solve this via substitution by isolating a variable, or we can solve via elimination by multiplying the second equation by either -14 or -11. I'm going to use substitution in this case:

c = 960 - a

 

14a + 11(960 - a) = 11490

Distribute:

14a + 10560 - 11a = 11490

Combine like terms:

3a + 10560 = 11490

Isolate a:

3a = 930

a = 310

 

Now to find c:

c = 960 - 310

c = 650

 

Now to check our answer:

14 * 310 +  11 * 650 = 11490

4340 + 7150 = 11490

11490 = 11490

 

All you have to do from here is write your answer as a sentence (or how you would say vocally how many of each tickets were sold).

Answer 2

Let A = # of adults

C = # of children

then

A + C = 960 or A = 960 - C

14A + 11C = 11490

substitue A into this equation

14(960-C) +11C = 11490

13440 - 14C +11C = 11490

-3C = -1950

C = 650

then from A = 960 + C = 310