Question

At SeptemberFest, the first dance of the year, the Students' Council charged $3 for couples and $2 for singles. If 365 tickets were sold and the total receipts were $925, how many single tickets were sold? Write you answers as a number only.

Answer 1

170

Explanation:

Given

Tickets = $2 per single and $3 per couple

Total tickets = 365

Total receipts = $925

Required

Number of singles tickets sold.

Let S and C represent singles and couples respectively.

If the total number of tickets sold is 365, then

S + C = 365 --- (1)

Also, if the singles are charged $2 and couples, $3, then

2S + 3C = 925 ----- (2)

Make C the subject of formula in (1)

C = 365 - S

Substitute 365 - S for C in (2)

2S + 3(365 - S) = 925

Open bracket

2S + 1095 - 3S = 925

Collect like terms

2S - 3S = 925 - 1095

-S = -170

Multiply both sides by -1

-1 * -S = -1 * -170

S = 170

Recall that S represents number of single present at the even.

Hence, the number of singles are 170