How would I solve this?ASB sells tickets to a dance for $10 to students who have an ASB sticker and $12 to those who don't have an ASB sticker. 160 tickets are sold and $1720 is raised. How many of each are sold?

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Answer 1 · 2017-10-28T13:06:22

$60$ $60$ people without an ASB sticker bought tickets.

$100$ $100$ people with an ASB sticker bought tickets.

We can set up a pair of simultaneous equations from the question:

Let $x =$ $x =$ the number of people with an ASB sticker that bought a ticket.

Let $y =$ $y =$ the number of people without an ASB sticker that bought a ticket.

1) $x + y = 160$ $" "x + y = 160 " "$ (the number of tickets sold)
2) $10 x + 12 y = 1720$ $" "10x + 12y = 1720 " "$ (the amount of money raised)

We can multiply the first equation by $10$ $10$ :

3) $10 x + 10 y = 1600$ $" "10x + 10y = 1600$

Then, subtract equation (3) from the equation (2):

$2 y = 120$ $2y = 120$

Therefore, $y = 60$ $y = 60$ , so $60$ $60$ people without an ASB sticker bought tickets.

Substitute $y = 60$ $y = 60$ into equation (1):

$x + y = 160$ $x + y = 160$

$x + 60 = 160$ $x + 60 = 160$

$x = 100$ $x = 100$

so $100$ $100$ people with an ASB sticker bought tickets.

Then, check your answer (optional):

$100 + 60 = 160 tickets sold$ $100 + 60 = "160 tickets sold"$

$(100 \cdot $ 10) + (60 \cdot $ 12) = $ 1000 + $ 720 = $1720 raised$ $(100 * $10) + (60 * $12) = $1000 + $720 = "$1720 raised"$