please help

Question

Jen Butler has been pricing? Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 105.Two adults and three children must pay $ 74.Find the price of the? adult's ticket and the price of a? child's ticket.

Answer 1

Let a be the price of an adult ticket and c the price of a child's ticket.

 

(1) 3a + 4c = 105

(2) 2a + 3c =  74

 

 

from (2), a = 37 - 1.5c

 

Substitute into (!):

 

3(37 - 1.5c) + 4c = 105

111 - 4.5c + 4c = 105

-.5c = -6

c = 12

 

Then a = 37 - 1.5c = 19

 

An adult ticket is $19 and a child ticket is $12

 

Answer 2

3a + 4c = 105

2a + 3c = 74

 

This looks like a perfect time for some elimination. Since neither the a's or c's are opposites, we can make them that way. Let's try the a's.

 

-2(3a + 4c) = -2(105)

 3(2a + 3c) = 3(74)

 

-6a - 8c = -210

 6a + 9c = 222

 

After adding the two together we get c = 12, because 6a + (-6a) = 0.

 

Hey, let's plug in our value for c to find a.

 

3a + 4(12) = 105

3a + 48 = 105

3a = 57

a = 19

 

Hope this helps!