Question

Tickets for a school event were $1.75 for students and $3.75 for parents. If a total of 62 tickets were sold for $178.50, how many student and parent tickets were sold? There were ___ student tickets sold and ____ parent tickets sold.

Answer 1

Work to solve p and s

Let s = students, s is in the place of x

Let p = parents, p is in the place of y

Answer:

There were 27 student tickets sold and 35 parent tickets sold

Explanation:

1. Use the system of equations by making two equations (one equation for the number of tickets sold and an other for the price the tickets): s + p = 62 and 1.75s + 3.75p = 178.50
2. Cancel out one of the variables by multiplying the first equation of the system (s + p = 62) by its inverse to cancel out; -1.75(s + p = 62) (to eliminate s) or -3.75(s + p = 62) (to eliminate p) to get -1.75s - 1.75p = -108.50 or - 3.75s - 3.75p = -232.50
3. Subtract the first equation from the second equation (to eliminate one variable either s or p) 1.75s + 3.75p = 178.50 - 1.75s - 1.75p - 108.50 that becomes 2p=70 (since both s cancel out) or 1.75s + 3.75p = 178.50 - 3.75s - 3.75p - 232.5 it becomes -2s = -54 (since both p cancel out)
4. Divide both sides by the coefficient of the variable so 2p/2 = 70/2 which is p = 35 or -2s/-2 = -54/-2 which is s = -27
5. Find the other variable value by substitute your known value and subtracting it on both sides: s + 35 -35 = 62 - 35 this equals to s = 27 or 27- 27 + p = 62 which equals to p = 35