Question

Mrs. Rodrigues was selling two kinds of raffle tickets for $1.50 and $3.50. The number of $1.50 tickets sold was 5 more than three times the number of $3.50 tickets sold. She earned a total of $1,607.50. How many $1.50 tickets were sold?

Answer 1

x = tickets

1.50(3x+5) +3.50x = 1607.50

4.50x +7.50 +3.50x = 1607.50

8.00x + 7.50 = 1607.50

8.00x = 1600

x = 1600/8 = 200 ( number of 3.50 tickets sold)

200*3 = 600+5 = 605

 there was 605 tickets sold for $1.50

Answer 2

The number of $1.50 tickets sold is 605

Represent the $1.50 tickets with x, and the $3.50 tickets with y

So, the equations are:

$x = 3y + 5$

$1.5x + 3.5y = 1607.5$

Substitute 3y + 5 for x in the second equation

$1.5(3y+5) +3.5y = 1607.50$

Open brackets

$4.5y +7.5 +3.5y = 1607.5$

Collect like terms

$4.5y +3.5y = 1607.5 - 7.5$

Evaluate the like terms

$8y = 1600$

Divide both sides by 8

$y = 200$

Recall that:

$x = 3y + 5$

So, we have:

$x = 3 \times 200 + 5$

$x = 605$

Hence, the number of $1.50 tickets sold is 605

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