A school is hosting a math fair. the event is very popular. on the first day 200 adults and 100 students attend. the amount of money paid at the door was $875. On the second day 50 adults and 30 students attended, with the amount of $227.50 paid at the door. If on the third and final day, they are expecting 150 adults and 200 students to attend, then how much money will be paid at the door

The sum of $875 would be paid at the door

Step-by-step explanation: Let the number of adults be a, and the number of students be b. On day one,  if 200 adults and 100 students paid a sum of $875 then we can express this as

200a +100b = 875

Then on day two, if 50 adults and 30 students paid a sum of $227.5 then we can express this too as

50a + 30b = 227.5

We now have a pair of simultaneous equations as follows;

200a + 100b = 875 (1)

50a + 30b = 227.5 (2)

We shall solve this by use of the elimination method. Multiply equation (1) by 30 and equation (2) by 100

6000a + 3000b = 26250 (3)

5000a + 3000b = 22750 (4)

Subtract equation (4) from equation (3)

1000a = 3500

Divide both sides of the equation by 1000

a = 3.5

We can now substitute for the value of a into equation (1)

200(3.5) + 100b = 875

700 + 100b = 875

Subtract 700 from both sides of the equation

100b = 175

Divide both sides of the equation by 100

b = 1.75

That means each adult paid $3.5 and each student paid $1.75. Therefore when 150 adults and 200 students attend the math fair, the money realized shall be calculated as follows;

150(3.5) +200(1.75) = x

525 + 350 = 875

The amount to be realized is therefore $875.