math question very difficut.?

Question

At a football game, 200 souvenirs were sold, some at $1.50 each and the rest $2.50 each. If the proceeds from the sales totaled $389, how many of each kind were sold?

Answer 1

if A is the number of souvenirs sold at $1.5 and B is the number of souveir sold at $2.50 then:

A + B = 200 (because there is a total of 200 souvenirs sold)

and 1.5*A + 2.5*B = 389 (because that is all the money collected.

you get 1.5*200 + B = 389 or B = 89 and A = 111

A quick check: the total is less than 2*200 meaning that they must have sold more items priced less than $2 than the sold items price more than $2.

Answer 2

X=# of $1.50 items
Y=# of $2.50items.

make a system of equations
X+Y=200 equation for total number of items sold
1.5*X+2.5*Y=389 equation for total sales. (# of items times price)

Solve one variable in terms of the other; usint the first:
X+Y=200 so
X=200-Y

plug 200-Y into the second equation for x and get:
300-1.5*Y+2.5*Y=389

and solve for Y. Then put that into the first equation and solve for X
Answer:
111 of the $1.50 items and 89 of the $2.50 items.

Answer 3

x= souvenirs sold at $1.50
y = souvenirs sold at $2.50

x + y = 200 > 1.50x +1.50y = 300

1.50x + 2.50y = 389

Now we just have to sold the system of two equations with 2 unknowns.
We subtract the second one from the first.
We get -y = -89 > y = 89
Now you replace y for its value in the first equation:

x + 89 = 200 > x = 111

Solution x = 111 and y = 89

Answer 4

let x be number at $1.50 each , then 200-x will be number at $2.50 each
so write 1.50x + (2.50)(200-x) = 389
solve this and get x = 111 (number of tickets at $1.50each)
200-111 = 89 (number of tickets at $2.50each)

Answer 5

let x be number at $1.50 each , then 200-x will be number at $2.50 each
so write 1.50x + (2.50)(200-x) = 389
solve this and get x = 111 (number of tickets at $1.50each)
200-111 = 89 (number of tickets at $2.50each)

Answer 6

x = # at 1.50
y = # at 2.50

1) x + y = 200
y = 200 - x

2) (1.50)x + (2.50)y = 389

(1.50)x + (2.50)(200 - x) = 389

(1.50)x + 500 - (2.50)x = 389

- x = - 111

x = 111

y = 200 - 111 = 89

Check

(1.50)(111) + (2.50)(89) = 389

166.50 + 222.50 = 389

389 = 389

Answer 7

let x be the number of tickets sold for $1.50
then (200-x) tickets sold for $2.50

The eq is
1.5x + 2.5(200-x) = 389
15x + 5000 - 25x = 3890
-10x = -1110
x = 111

sold 111 tickets for $1.5 and 89 for $2.5

Answer 8

let x = souv.for $1.50 and y = those for $2.50

total souveniers: x + y = 200
money made: 1.5x + 2.5 y = 389

Solve the system.