Question

Each adult paid 75 cents and each student paid 50 cents at the schoot play. A total of 750 attended. How many adults attended if the receipts totaled $437.50?

Answer 1

Answer:

250 adults

Step-by-step explanation:

With the information of the problem we have a system of two linear equations:

$x+y=750$

$0.75x+0.50y=437.50$

Where x represent the quantity of adults and y represent the student. Solving the first equation for x we have:

$x+y=750\\x=750-y$

Using this result in the second equation:

$0.75x+0.50y=437.50\\0.75(750-y)+0.50y=437.50\\562.5-0.75y+0.50y=437.50\\-0.25y=437.50-562.5\\-0.25y=-125\\0.25y=125\\y=\dfrac{125}{0.25}\\y=500$

With this result we know that we have 500 students, using the result of y in the first equation we will find the answer for x then:

$x+y=750\\x+500=750\\x=750-500\\x=250$

Then the we have 250 adults.