At school Spencer is selling tickets to the Little Mermaid play. The first day of ticket sales sold 5 senior citizen tickets and 4 child tickets for a total of $22. The school took in $54 with 24 senior citizen tickets and 2 child tickets. Create a system of equations based on the problems and find the cost of child tickets and senior tickets.

Step-by-step explanation:

Let A be cost of adult ticket

Let C be cost of child ticket

5A + 4C = 22

A = (22 - 4C)/5

                24A + 2C = 54

24((22 - 4C)/5) + 2C = 54

 105.6 - 19.2C + 2C = 54

                     - 17.2C = - 51.6

                            C = $3.00

A = (22 - 4(3))/5 = $2.00

Step-by-step explanation:

Let,

Senior tickets = x

Child tickets = y

In case 1

5x + 4y = 22 (1)

In case 2

24x + 2y = 54

On multiplying both sides by 2

48x + 4y = 108 (2)

On subtracting 1 and 2

48x + 4y - (5x + 4y) = 108 - 22

48x + 4y - 5x - 4y = 86

43x = 86

x = 86/43

x = 2

From 1

5(2) + 4y = 22

10 + 4y = 22

4y = 22 - 10

4y = 12

y = 12/4

y = 3

Hence,

Cost of 1 child ticket = $ 2

Cost of 1 adult ticket = $ 3

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.

~

30005

yes ok