SOLUTION: the johnson family and the gonzalez family went to the movies together. the johnson family bought 4 adult tickets and 2 child tickets for a total of $37. the gonzalez family bought
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Question 1070675: the johnson family and the gonzalez family went to the movies together. the johnson family bought 4 adult tickets and 2 child tickets for a total of $37. the gonzalez family bought 3 adult tickets and 4 child tickets for a total of 39$ what is the price of each type of ticket (adult and child) at this theater ? Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! Johnsons: 4a+2c = 37
Gonzalez: 3a+4c = 39
We can solve by substitution or elimination. I'll do it by elimination because I suspect that's what your teacher expects you to do:
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4a+2c = 37 multiply all times -2 and add to the next equation
:
3a+4c = 39
+
-8a-4c = -74
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-5a+0c = -35
-5a = -35 divide both sides by -5, and remember that -/- = +
a = 7 the adult tickets are 7.
:
Now we solve for c:
4a+2c = 37 multiply all times 3
3a+4c = 39 multiply all times -4 and add to the other equation
:
12a+6c = 111
+
-12a-16c = -156
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0a-10c = -45
-10c = -45
c = 4.50 this is the cost of a child's ticket
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Let's check:
Johnson: 4(7)+2(4.5) = 37 Correct
Gonzalez: 3(7)+4(4.5)= 39 Also correct.
:
john
