Solve this application problem using a system of equations: the springfield movie theater sold adult tickets for $4.10 each and children's tickets for $2.70 each. last thursday, a total of $331.30 was collected from 89 movie watchers. how many of each type of ticket were sold on thursday?

65 adult ticket and 24 children's ticket

Step-by-step explanation:

Let the total number of adults be x

And the total number of children be y

The cost of ticket for 1 adult = $4.10 , this means that the cost of ticket for x adults will be 4.10x

The cost of ticket for a child = $2.70 , this means that the cost of ticket for y children will be 2.70y.

The total sale was $331.30 , that is

4.10x + 2.70y = 331.30

Total number of movie watchers were 89 , that is

x + y = 89

Combining the two equations , we have :

x + y = 89 equation 1

4.10x + 2.70y = 331.30 equation 2

solving the system of linear equation by substitution method.

From equation 1 , make x the subject of the formula

x = 89 - y equation 3

substitute x = 89 - y into equation 2 , equation 2 then becomes

4.10(89 - y ) + 2.70y = 331.30

expanding the bracket , we have

364.9 - 4.10y + 2.70y = 331.30

364.9 - 1.4y = 331.30

collecting the like terms , we have

364.9 - 331.30 = 1.4y

33.6 = 1.4y

divide through by 1.4

33.6/1.4 = y

Therefore : y = 24

substitute y = 24 into equation 3

x = 89 - y

x = 89 - 24

x = 65

Therefore , there were 65 adults and 24 children ticket sold

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation:

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58