The manager at a community pool is looking over receipts. On a certain Monday, the pool had 41 children and 28 adults, which brought in $222. That same week on Tuesday, 14 children and 21 adults came to the pool, which brought in $133. What are the admission prices for children and adults?
45
To determine the admission prices for children and adults, we can set up a system of equations based on the given information. Let's assume the admission price for children is 'c' dollars and for adults is 'a' dollars.
From the first day, we know that 41 children and 28 adults came to the pool, bringing in a total of $222. This can be represented as the equation:
41c + 28a = 222 (equation 1)
From the second day, we know that 14 children and 21 adults came to the pool, bringing in a total of $133. This can be represented as the equation:
14c + 21a = 133 (equation 2)
Now we need to solve this system of equations to find the values of 'c' and 'a'. We can use the method of substitution or elimination to solve the system. Let's use the elimination method here:
Multiplying equation 1 by 14 and equation 2 by 41 to eliminate the 'c' term, we get:
574c + 392a = 3116 (equation 3)
574c + 861a = 5569 (equation 4)
Now, subtracting equation 3 from equation 4, we eliminate the 'c' term:
(574c + 861a) - (574c + 392a) = 5569 - 3116
861a - 392a = 2453
469a = 2453
Dividing both sides of the equation by 469, we can find the value of 'a':
a = 2453 / 469
a ≈ 5.22
Now we can substitute the value of 'a' into equation 1 to find the value of 'c':
41c + 28(5.22) = 222
41c + 146.16 = 222
41c = 222 - 146.16
41c = 75.84
Dividing both sides of the equation by 41, we can find the value of 'c':
c = 75.84 / 41
c ≈ 1.85
Therefore, the admission price for children is approximately $1.85 and for adults is approximately $5.22.
Use what they told you:
41c+28a = 222
14c+21a = 133
Now just solve for c and a