Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $102. Two adults and three children must pay $72. Find the price of the adult's ticket and the price of a child's ticket.
BeeLiz19
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Let x be the amount of each ticket for an adult.
Let y be the amount of each ticket for a child.
three adults at x value AND four children at y value IS 102
3x + 4y = 102
two adults at x value AND three children at y value IS 72
2x + 3y = 72
Rearrange one of the equations to solve for a variable:
2x + 3y = 72
3y = -2x + 72
y = -2/3x + 24
Now we can plug this new equation into the one we haven't touched yet:
3x + 4y = 102
3x + 4(-2/3x + 24) = 102
3x - 8/3x + 96 = 102
9/3x - 8/3x = 102 - 96
1/3x = 6
Dividing by 1/3 is the same as multiplying by 3/1:
x = 18
Plug this into the equation solving for y:
y = -2/3x + 24
y = -2/3(18) + 24
y = -36/3 + 24
y = -12 + 24
y = 12
THEREFORE adult tickets cost $18 and kids tickets cost $12.
?
3A+4C = 102
2A+3C = 72
3A+4.5C = 108
0.5C = 6
C = $12
A = $18