Georgia Connections Academy is selling tickets to its Spring Fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold. (7 points)
A. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.
_____a+_____s=_____
B. 900 tickets are sold for the spring fling. Write an equation to represent this situation.
a+____=_____
C. Use the above system of equations to determine how many adult and student tickets were sold.
___ adult tickets and ______ student tickets were sold
A. The equation that represents this situation to find the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
B. Since 900 tickets are sold for the spring fling, the equation to represent this situation is:
a + s = 900
C. To determine how many adult and student tickets were sold, we need to solve the system of equations:
4a + 2.50s = 2820
a + s = 900
From equation B, we can rewrite it as a = 900 - s. Substituting this into equation A, we get:
4(900 - s) + 2.50s = 2820
Simplifying, we have:
3600 - 4s + 2.50s = 2820
-1.50s = -780
s = 520
Substituting this value of s back into equation B, we get:
a + 520 = 900
a = 900 - 520
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
A. The equation that represents the situation to find the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
B. The equation to represent the situation where 900 tickets are sold for the spring fling is:
a + s = 900
C. To determine how many adult and student tickets were sold, we can solve the system of equations formed in parts A and B.
From equation B, we have:
a + s = 900
Rearranging equation B, we get:
a = 900 - s
Substituting this value of a into equation A, we get:
4(900 - s) + 2.50s = 2820
Expand and solve the equation:
3600 - 4s + 2.50s = 2820
Combine like terms:
-1.50s = -780
Divide by -1.50:
s = 520
Substituting this value of s back into equation B, we can find the value of a:
a + 520 = 900
a = 900 - 520
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
A. To write an equation that represents this situation, we can use the given information. Let's say the number of adult tickets sold is "a" and the number of student tickets sold is "s". The cost of each adult ticket is $4, so the total cost of adult tickets sold would be 4a. Similarly, the cost of each student ticket is $2.50, so the total cost of student tickets sold would be 2.50s. The school makes a total of $2,820, so the equation would be:
4a + 2.50s = 2820
B. Since 900 tickets are sold for the spring fling, we know that the total number of tickets sold is 900. We can write the equation as:
a + s = 900
C. To determine how many adult and student tickets were sold, we need to solve the system of equations from parts A and B. We can solve this system by substitution or elimination. For simplicity, let's use the substitution method:
From equation B, we can rewrite it as:
s = 900 - a
Now substitute this value in equation A:
4a + 2.50(900 - a) = 2820
Simplifying the equation:
4a + 2250 - 2.50a = 2820
1.5a + 2250 = 2820
1.5a = 2820 - 2250
1.5a = 570
Divide both sides of the equation by 1.5:
a = 570 / 1.5
a = 380
Now substitute this value back into equation B to find the value of s:
s = 900 - a
s = 900 - 380
s = 520
Therefore, 380 adult tickets and 520 student tickets were sold.