$9099 worth of tickets are sold. adult tickets are $8 a person. students are $6 a person. children are $5 a person. 102 more adult ticket are sold than students tickets. two times more student tickets are sold than children tickets. how many children tickets were sold

The Answer is: There were 604 adult tickets sold and 502 student tickets sold and 251 children tickets sold.

Step-by-step explanation:

Let a = the number of adult tickets. Let s = the number of student tickets. Let c = the number of children tickets sold. The total of all tickets sold is equal to $9,099. Equation below:

8a + 6s + 5c = $9,099

There are 102 more adult tickets than students. Equation below:

a = s + 102

There are twice as many student tickets than children tickets. Equation below:

c = s/2

By substitution, solve the equation:

8a + 6s + 5c = $9,099

8(s + 102) + 6s + 5(s/2) = 9099

8s + 816 + 6s + 5s/2 = 9099

14s + 5s/2 = 9099 - 816

14s + 5s/2 = 8283

28s + 5s = 16566

33s = 16566

s = 502  student tickets.

Solve for a:

a = s + 102 = 502 + 102 = 604 adult tickets.

Solve for c:

c = s/2 = 502 / 2 = 251 children tickets.

Proof:

8(502 + 102) + 6(502) + 5(251) =  

8(604) + 6(502) + 5(251) =  

4832 + 3012 + 1255 = 9099

9099 = 9099

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

answer: what in the world is this

step-by-step explanation: