please asnwer and explain?

Question

mary sold 105 tickets for the basketball game. each adult ticket costs 2.50$ and each student ticket costs 1.10$ mary collected $221.90. how many of each kind of ticket did she sell?

Answer 1

(105-x)*1.10 +x*2.50=221.90
115.50-1.10x+2.50x=221.90
1.40x=106.4
x=76 tickets sold to students and 31 tickets sold to adults.

Answer 2

So first you know the that the total student tickets sold times the price of each student ticket is the total for that. Then the same would b said for adult tickets. You also know the total amount made.

So ($1.10) * (x) + ($2.50) * (y) = $221.90

X is the number of student tickets sold and y is the number of adult tickets sold.

Now we make another equation

x + y=105

Because if x and y represent tickets for each adult and student sold together they represent total amount of tickets sold.

Now we have 2 equations

x + y = 105

($1.10) * (x) + ($2.50) * (y) = $221.90

We want only 1 variable left so we multiply the top by 1.1

1.1x +1.1y = 115.5

Now we subtract this equation by the one with the total money made

($1.10) * (x) + ($2.50) * (y) = $221.90
- (1.1x +1.1y = 115.5)

We receive

1.4y=106.4

We divide and we receive

y= 76

Then we plug in 76 for y and figure out x

x + 76= 105

x=29

So in conclusion

29 student tickets sold
76 adult tickets sold

Answer 3

x+y= 105, these are added together because you want to find out how many of each she sold.

2.5x+1.1y=221.9, this equation models the the two ticket totals added together. On these type of problems, money always goes together.

You use substitution for this problem. Make the first equation a slope-intercept equation: y=-x+105. Plug this in for y in the second problem.

2.5x+1.1(-x+105)=221.9. Solve this equation for X. Once worked out, you will get X=76. So, Mary sold 76 $2.50 tickets. Now you must plug that back in to the original equation.

76 + y= 105, y= -76 + 105, y =29. So, Mary sold 39 $1.10 tickets.

Hope this helps!

Evan

Answer 4

Cost of adult ticket A=2,50
Cost os student ticket S=1,10
Number of adult tickets Na
Number of student tickets Ns
Na + Ns = 105 then Ns = 105 - Na
2,50Na + 1,10Ns = 221,90
2,50Na + 1,10(105 – Na) = 221,90
(2,50 – 1,10)Na + 1,10(105) = 221,90
Na = (221,90 – 115.5)/1,40
Na = 76 then Ns = 29

Answer 5

let a be the number of adult tickets
Let s be the number of student tickets
Then:
a + s = 105
2.50a + 1.10s = 221.90
Multiply top by -2.50 and add:
-2.50a - 2.50s = -105(2.50) = -262.50
2.50a + 1.10s = 221.90
Now add:
-1.40s = -40.60
s = 40.60/1.40 = 29
Going back to the first equation: a + s = a + 29 = 105
a = 105 - 29 = 76

Answer 6

Ok, we need two equations.
1. A + C = 105, since adult tickets plus children tickets = 105
2. 2.5A + 1.1C = $221.90

I would use elimination
1. -2.5A + -2.5C = - 262.50
2. 2.5A + 1.1C = 221.90

-1.4C = -40.6
c = 29, so A = 76