Tickets to science exposition cost $5.75 each for students and $7.00 for adults. How many students and adults went if the ticket charge was $42.75?

5*5.75 + 2*7.00 = 42.75

5 students and 2 adults

5 students 2 adults

thx

Barbara bought 5 amusement park tickets at a cost of $30. If she bought 7 tickets, how much would it cost?

ths so much

thanks you so much

Tickets to a science exposition costc5.75 for students and 5.75 for adults how many students and how many adults went

THX FOR HELPING!

To solve this problem, we can set up a system of equations based on the given information. Let's let "s" represent the number of student tickets and "a" represent the number of adult tickets.

According to the problem, the total charge for the tickets was $42.75. Since each student ticket costs $5.75 and each adult ticket costs $7.00, we can write the equation:

5.75s + 7.00a = 42.75

We also know that the number of tickets sold should add up to the total number of attendees. So the equation can be written as:

s + a = total number of attendees

However, we don't have the total number of attendees, so we can't solve it directly. We need another equation to solve the system.

Let's rearrange the equation s + a = total number of attendees to solve for s:

s = total number of attendees - a

Now we substitute this value of s into the first equation:

5.75(total number of attendees - a) + 7.00a = 42.75

Next, distribute 5.75 on the left side:

5.75 * total number of attendees - 5.75a + 7.00a = 42.75

Combine like terms:

-5.75a + 7.00a = 42.75 - 5.75 * total number of attendees

1.25a = 42.75 - 5.75 * total number of attendees

Now, we can solve this equation to find the value of "a" and then substitute it back into one of the original equations to find "s".

We know that the number of attendees cannot be a fraction, so we will look for a value of "a" that gives us a whole number for "s".

Let's take the values of "a" starting from 1 and plug them into the equation:

For a = 1:
1.25(1) = 42.75 - 5.75 * total number of attendees
1.25 = 42.75 - 5.75 * total number of attendees
5.75 * total number of attendees = 42.75 - 1.25
5.75 * total number of attendees = 41.50
total number of attendees = 41.50 / 5.75 ≈ 7.22

For a = 2:
1.25(2) = 42.75 - 5.75 * total number of attendees
2.50 = 42.75 - 5.75 * total number of attendees
5.75 * total number of attendees = 42.75 - 2.50
5.75 * total number of attendees = 40.25
total number of attendees = 40.25 / 5.75 ≈ 7

For a = 3:
1.25(3) = 42.75 - 5.75 * total number of attendees
3.75 = 42.75 - 5.75 * total number of attendees
5.75 * total number of attendees = 42.75 - 3.75
5.75 * total number of attendees = 39
total number of attendees = 39 / 5.75 ≈ 6.78

For a = 4:
1.25(4) = 42.75 - 5.75 * total number of attendees
5 = 42.75 - 5.75 * total number of attendees
5.75 * total number of attendees = 42.75 - 5
5.75 * total number of attendees = 37.75
total number of attendees = 37.75 / 5.75 ≈ 6.57

For a = 5:
1.25(5) = 42.75 - 5.75 * total number of attendees
6.25 = 42.75 - 5.75 * total number of attendees
5.75 * total number of attendees = 42.75 - 6.25
5.75 * total number of attendees = 36.50
total number of attendees = 36.50 / 5.75 ≈ 6.35

From the above calculations, it seems that for a = 2, we get a "total number of attendees" that is closest to a whole number, 7.

Therefore, if we assume that 2 adults attended (a = 2), then we can substitute this value into one of the original equations to find "s":

s + 2 = 7 (assuming 2 adults attended)
s = 7 - 2
s = 5

So, 5 students and 2 adults attended the science exposition.