Atheater sells tickets for a concert. tickets for lower-level seats cost $35 each. tickets for upper-level seats cost $25 each. the theater sells 350 tickets for $10,250. how many types of each ticket were sold?

The Answer is: Lower Level seats = 150. Upper level seats = 200.

Step-by-step explanation:

Start with two known equations:

1 - the number of Lower Level times 35 + the number of Upper level times 25 = the total dollar amount of $10,250.

35L + 25u = 10250

The number of both types of tickets = 350

L + u = 350

Solve for u:

u = 350 - L

Substitute and solve for L, Lower level seats:

35L + 25(350 - L) = 10250

35L + 8750 - 25L = 10250

10L + 8750 = 10250

10L = 1500

L = 150

There are 150 Lower Level seats.

u = 350 - L

Subtract to get the number of upper level seats:

u = 200

Proof:

35(150) + 25(200) =

$5,250 + $5,000 = $10,250

number of lower-level seat tickets =150

number of upper-level seat tickets =200

Step-by-step explanation:

Let number of lower-level seat tickets be x

Let number of upper-level seat tickets be y

Total number of tickets sold by the theatre = 350

x +y = 350 - - - - - 1

Tickets for lower-level seats cost $35 each.

Tickets for upper-level seats cost $25

Cost of x low-level seat tickets = 35x

Cost of upper-level seat tickets = 25y

Total cost of seat tickets =Lower- level seat tickets + upper-level seat tickets

35x + 25y =10250 - - - - - -2

From equation 1

x = 350 -y

Put x = 350 -y in equation 2

35(350-y) + 25y =10250

12250-35y + 25y = 10250

-10y = 10250 -12250 = -2000

y = 2000/10 = 200

x = 350-y = 350-200= 150

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step-by-step explanation:

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2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.