word problem help??

Question

If you have made $208 selling 56 raffle tickets, how many were $5 tickets, and how many were $2 tickets?

Answer 1

x = $5 tickets
y = $2 tickets

x + y = 56
5x + 2y = 208

Now just solve the system to find x and y
y = 56 - x
Substitute that in the second equation:
5x + 2(56-x) = 208
5x + 112 - 2x = 208
3x = 96
x = 32

Replace x by its value in the any of the equations:
32 + y = 56
y = 56 - 32
y = 24

Answer 2

You have 2 equations and two unkowns.
Call the $5 tickets x, and the $2 tickets y.
You know that the number of $5 tickets and the number of $2 tickets sum up to 56, so x + y =56
You also know that 5x + 2y = 208
You can use the elimination method or substitution.
You should get 32 $5 tickets and 24 $2 tickets.

Answer 3

let x equals # of $5 tickets and y = # of $2 tickets

x + y = 56 total number of tickets
5x + 2y = 208 total costs

solve
2x + 2x = 112
3x = 96
x = 32
y = 56 - 32 = 24

check 5*32 + 2*24 = 208

Answer 4

let x be the number of $2 tickets and y be the number of $5 tickets

then we can have two equations
1. x + y = 56
and
2. 2(x) + 5(y)=208

solving them simultaneously will give the answer

let x be the subject of eq 1
then we get
x = 56 - y
substitute for x in eq 2
2( 56 - y) + 5y = 208
112 - 2y + 5y = 208
112 + 3y = 208
3y= 208- 112
3y=96
y= 96/3
y=32

substitute this value for y into any of the original eq giving
x+ 32 = 56
x=56-32
x=24

therefore the number of $2 tickets was 24 and the number of $5 tickets was 32

you can always check the answer

Answer 5

If by "made" you mean sales and not profits:

f = # of five dollar tickets
t = # of two dollar tickets

f + t = 56
5f + 2t = 208

solve for f in terms of t using the first equation
f = 56 - t

Now substitute 56 - t for f in the second equation
5(56 - t) + 2t = 208 ----- distribute the 5 to get. . .
280 - 5t + 2t = 208 ----- combine like terms to get. . .
280 -3t = 208 ------------ subtract 208 from both sides to get. . .
72 -3t = 0 ----------------- add 3t to both sides to get. . .
72 = 3t -------------------- divide both sides by 3 to get. . .
24 = t <===== there's t

Now plug 24 into t into either of the two equations -- I'm choosing the first one because it's easiest

f + t = 56
f + 24 = 56 -------------- subtract 25 from both sides to get. . .
f = 32 <========= there's f

so. . .
you sold 32 $5 tickets for a total of $160
you sold 24 $2 tickets for a total of $48

$160 + $48 = $208 <==== check!
32 + 24 = 56 tickets sold <======= check!

Answer 6

a + b = 56
5a + 5b = 280
also 5a + 2b = 208
subtracting we get 3b = 72 => b = 24
and a = 56 -- b = 56 -- 24 = 32
32 $5 tickets and 24 $2 tickets.