SOLUTION: Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $122. Two adults and three children must pay $87. Find the
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-> SOLUTION: Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $122. Two adults and three children must pay $87. Find the
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Question 283672: Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $122. Two adults and three children must pay $87. Find the price of the adult's ticket and the price of a child's ticket. Answer by JenniferTutors(83) (Show Source):
You can put this solution on YOUR website! In this word problem, I pulled out two equations:
Three adults and four children pay 122:
a = adults
c = children
3a + 4c = 122
Two adults and three children pay 87:
2a + 3c = 87
I used the Elimination Method to solve by subtracting the equations:
Better form this way, Subtract:
3a + 4c = 122
2a + 3c = 87
a + c = 35
Now you can subtract one of the variables to the other side to get one by itself, either variable is fine:
Now place the value of c into the first equation:
Combine the a's (like terms)
Subtract the 140 from the left to the right side of the equation:
Divide by a negative 1 to get a positive and to both sides:
Now you have the value of tickets for adults. You can place the value of a into the second equation to solve for c.
Subtract the 36 from the left to right side of the equation:
Divide 3 into itself and the right side:
If you Check: adults = 18, children = 17
Place the values into the first equation:
