math ratio question

Question

if there is 189 tickets and all and there is a ratio of 4:5 / four student tickets to five adult tickets . each student ticket is $5 and each adult ticket is $7 what is the amount of student tickets and adult tickets sold

Answer 1

We know that there are a total of 189 tickets sold, and that for every 4 student tickets sold, there were 5 adult tickets sold. Let's express this ratio in terms of a fraction, so we can more easily implement it into an equation.

Since there were 4 student tickets for every five adult tickets, that means that 4 out of every 9 tickets sold was a student ticket (because 4 + 5 = 9). This means that 4/9 of total tickets sold were student tickets. We can express this as an equation (remember that "of" usually indicates multiplication and "is" or "were" indicates equals):

(4/9)*(total tickets sold) = (student tickets sold)

We know the number of total tickets sold is 189, so we can plug that in to our equation:

(4/9) * 189 = (student tickets sold)

84 = (student tickets sold)

Now we have part of our answer: there were 84 student tickets sold. But, how many adult tickets were sold?

We can figure this out since we know that the (number of student tickets sold) + (number of adult tickets sold) = (total number of tickets sold). Plugging in the total number of tickets and the number of student tickets:

84 + (adult tickets) = 189

We can find the number of adult tickets by subtracting 84 from both sides.

84 + (adult tickets) - 84 = 189 - 84

(adult tickets) = 105

In total, there were 84 student tickets sold and 105 adult tickets sold.

We can check our work to make sure that the ratio of 84:105 simplifies to our original 4:5. Since 84:105 is 4:5 times 21, we can see that the ratios are proportional.