Final answer:
To find out how many raffle tickets Jordan and Caroline sold, we set up a proportion based on the given ratio and the information that Jordan sold 30 more tickets. Caroline sold 45 tickets and Jordan sold 75 tickets.
Step-by-step explanation:
The question involves solving a problem where Jordan and Caroline sold raffle tickets for a fundraiser with a specific ratio between the number of tickets they sold. For every 10 tickets Jordan sold, Caroline sold 6. If Jordan sold 30 more tickets than Caroline, we can set up a proportion to find out the number of tickets each person sold.
Step-by-step Solution
Let the number of tickets Caroline sold be x.
According to the given ratio, Jordan sold 10 tickets for every 6 tickets Caroline sold. This can be expressed as Jordan selling (rac{10}{6})x tickets.
It was also given that Jordan sold 30 more tickets than Caroline, so the equation can be set up as (rac{10}{6})x = x + 30.
Multiplying both sides by 6 to clear the fraction, we get 10x = 6x + 180.
Simplifying the equation by subtracting 6x from both sides, we find 4x = 180.
Divide both sides by 4 to find the value of x, which gives us x = 45.
Caroline therefore sold 45 tickets. To find out how many Jordan sold, we substitute x into the equation for Jordan's tickets (rac{10}{6})x which equals (rac{10}{6}) imes 45 = 75 tickets.
So, Caroline sold 45 tickets and Jordan sold 75 tickets.