292 tickets were sold for a high school basketball game. An adult ticket cost $3.00. A student ticket costs $1.00. Ticket sales were $470.00. How many adult tickets were sold
s + a = 292
1.00 s + 3.00 a = 470
s = 292 - a
1 (292 - a) + 3 a = 470
292 + 2 a = 470
2 a = 470 - 292 etc
To find the number of adult tickets sold, we can set up a system of equations.
Let's assume the number of adult tickets sold is 'a,' and the number of student tickets sold is 's.'
From the given information, we know that a + s = 292 (equation 1) since the total number of tickets sold is 292.
We also know that the total ticket sales amount is $470.00. With adult tickets priced at $3.00 and student tickets priced at $1.00, we can write another equation:
3a + 1s = 470 (equation 2)
Now, we can solve this system of equations using substitution or elimination. Let's use the elimination method.
First, let's multiply equation 1 by 3 to align the coefficients of 'a':
3(a + s) = 3(292)
3a + 3s = 876 (equation 3)
Now we can subtract equation 2 from equation 3 to eliminate 's':
(3a + 3s) - (3a + 1s) = 876 - 470
3a + 3s - 3a - s = 406
2s = 406
s = 406/2
s = 203
So, 203 student tickets were sold.
Now, we can substitute the value of 's' back into equation 1 to find the number of adult tickets:
a + 203 = 292
a = 292 - 203
a = 89
Therefore, 89 adult tickets were sold.