You and your friend are selling tickets to a charity event. You sell 4 adult tickets and 11 student tickets for $148. Your friend sells 7 adult tickets and 5 student tickets for $145. What is the cost of a student ticket?
$
1.45
@ vera .... Just blurting out an answer serves absolutely no purpose!
4a + 11s = 148
7a + 5s = 145
solve the 2 equations in 2 unknowns
I suggest multiplying the first by 7 and the 2nd by 5 and then subtracting them
Apparently Vera in Pleasanton wants everyone to know about her ignorance.
To find the cost of a student ticket, we can set up a system of equations based on the information given.
Let's assume that the cost of an adult ticket is A and the cost of a student ticket is S.
From the first sentence, we know that you sell 4 adult tickets and 11 student tickets for a total of $148. This can be expressed as the equation:
4A + 11S = 148
From the second sentence, we know that your friend sells 7 adult tickets and 5 student tickets for a total of $145. This can be expressed as the equation:
7A + 5S = 145
Now we have a system of two equations with two variables. We can solve this system to find the values of A and S.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution in this case.
Let's solve the first equation for A:
4A + 11S = 148
4A = 148 - 11S
A = (148 - 11S)/4
Now substitute this expression for A in the second equation:
7A + 5S = 145
7((148 - 11S)/4) + 5S = 145
Simplify this equation:
37S - 11S^2 + 20S = 580
-11S^2 + 57S = 580
Rearrange the equation and set it equal to zero:
11S^2 - 57S + 580 = 0
This is a quadratic equation. We can solve it by factoring or using the quadratic formula. In this case, factoring the equation doesn't yield integer solutions, so let's use the quadratic formula:
S = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we get:
S = (-(-57) ± √((-57)^2 - 4(11)(580))) / (2(11))
= (57 ± √(3249 - 25480)) / 22
Simplifying further:
S = (57 ± √(-22231)) / 22
Since the square root of a negative number is not a real number, there are no real solutions for S. Therefore, we cannot determine the cost of a student ticket based on the given information.