The cost for a child is $ , and the cost for an adult is $

Question

Emma is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered 2 child buffets and 3 adult buffets, which cost a total of $99. At another table, the customers ordered 3 child buffets and 3 adult buffets, paying a total of $114. How much does the buffet cost for each child and adult?

Answer 1

2c + 3a = 99    AND   3c + 3a = 114

subtract 2c and 3c from the left sides of these equations and you get:

3a = 99 - 2c   AND   3a = 114 - 3c

Since 3a = both 99 - 2c AND 114 - 3c we can also state this:

99 - 2c = 114 - 3c

add + 2c to both sides of equation results in:

99 = 114 - c

add +c to both sides of the equation results in:

99 + c = 114

subtract 99 from both sides of the equation results in:

c = 15

 

Go back to the first equation:  2c + 3a = 99

plug in '15' for 'c' and equation becomes:

30 + 3a = 99

subtract 30 from both sides results in:

3a = 69

divides both sides by 3 results in:

a = 23

 

So, adults each paid $23 and children each paid $15