SOLUTION: Tickets for the father and son breakfast were 2 dollars for fathers and 1.50 dollars for sons. If a total of of 75 tickets were sold for 127.50 dollars, how many fathers and how ma

Click here to see ALL problems on Miscellaneous Word Problems

Question 566545: Tickets for the father and son breakfast were 2 dollars for fathers and 1.50 dollars for sons. If a total of of 75 tickets were sold for 127.50 dollars, how many fathers and how many sons attended the breakfast?

Found 3 solutions by stanbon, mananth, radium:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Tickets for the father and son breakfast were 2 dollars for fathers and 1.50 dollars for sons. If a total of of 75 tickets were sold for 127.50 dollars, how many fathers and how many sons attended the breakfast?
---------------------------------
Equations:
f + s = 75 tickets
2f+1.5s = 127.50
---------
Multiply thru the 1st by 2 to get:
2f + 2s = 150
2f +1.5s = 127.50
-----
Subtract and solve for "s":
0.5s = 22.5
s = 45 (# of son's tickets sold)
-----
Solve for "f":
f + s = 75
f + 45 = 75
f = 30 (# of father's tickets sold)
=====================================
Cheers,
Stan H.
========================

Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
Fathers x
Sons y

1 x + 1 y = 75 .............1
2 x + 1.5 y = 127.5 .............2
Eliminate y
multiply (1)by -1.5
Multiply (2) by 1
-1.5 x -1.5 y = -112.5
2 x 1.5 y = 127.5
Add the two equations
0.5 x = 15
/ 0.5
x = 30
plug value of x in (1)
1 x + 1 y = 75
30 + 1 y = 75
1 y = 75 -30
1 y = 45
y = 45
Fathers 30
Sons 45
m.ananth@hotmail.ca

Answer by radium(1)   (Show Source):
You can put this solution on YOUR website!
This can be solved with 1 variable as well!

The equation
---------------
1.5x + 2.00(75 - x) = 127.5

We let x represent the number of sons tickets. We know that that the number of father tickets must be (75 - x). We know that the sons tickets are $1.50 each and the fathers tickets are $2.00 each. So we arrange our equation accordingly.
1.5x + 2.00(75 - x) = 127.5.

Using the distributive property we get: 1.5x + 150 - 2x = 127.5
Combining like terms gives us: -.5x=-22.5
Dividing both sides by -.5 gives us: x = 45
45 of sons tickets were sold, to find the amount of fathers we simply subtract 45 from 75 which gives us 30, the amount of fathers tickets sold.