Question

Daniel and Rosa are ticket-sellers at their class play, Daniel handling student tickets that sell for $2.00 each and Rosa selling adult tickets for $6.50 each. If their total income for 22 tickets was $102.50, how many did Daniel sell?
9
11
13
18

Answer 1

HI!!

Answer 2

Hello :)

Answer 3

lets call the number of daniel's tickets \(x\) so the number of rosa's is \(22-x\) (since they add to 22)

Answer 4

daniel's $2 bring (2x\) dollars, and rosa's $6.50 tickets bring \(6.50(22-x)\) dollars

Answer 5

since the total is $102.50 you can solve \[2x+6.5(22-x)=102.5\] for \(x\)

Answer 6

do you know how to do that?

Answer 7

distribute right?

Answer 8

yes that is first

Answer 9

then combine like terms

Answer 10

if it was me, i would just cheat

Answer 11

http://www.wolframalpha.com/input/?i=2x%2B6.5(22-x)%3D102.5

Answer 12

thanks!

Answer 13

\[\color\magenta \heartsuit\]

Answer 14

If you're going to cheat, then you can solve this without even writing an equation.
Since 22 tickets were sold, then 22 minus the number Daniel sold is the number Rosa sold.
Look at the choices.
A. Daniel sold 9 tickets.
Then Rosa sold 22 - 9 = 13 tickets.
Now use the cost of the tickets to see if using these numbers of tickets sold will add to $102.50
9 student tickets: 9 * $2 = $18
13 * $6.50 = $84.50
$18 + $84.50 = $102.50
Since the first choice gives the correct total, then the answer is Daniel sold 9 tickets.