There were 429 people at Bingo Night. Admission was $1 for adults and 75 cents for children.

Question

There were 429 people at Bingo Night. Admission was $1 for adults and 75 cents for children. The receipts totaled $372.50. How many adults and how many children attended the event?

Answer 1

Hi Chris

 

This is a classic algebra substitution problem.  We need to make two equations that we can rearrange to solve for the variables.  Let's start by setting the number of adults as "A" and the number of children as "C".

 

From the first sentence, we know A + C = 429.

 

From the second sentence, we know that adult tickets were $1 and child tickets were $0.75.  The total ticket was $372.50 so:

 

$1*A + $0.75*C = $372.50

 

First we need to rearrange the first equation to solve for one of the variables. Let's solve for A:

A + C = 429,  subtract C from both sides to get A = 429 - C

 

Now we plug the value of A in the second equation:

($1 *(429-C)) + $0.75*C = $372.50        Now we distribute the first part to get:

$429 - $1*C + $0.75*C = $372.50          Next we combine like terms:

$429 - $0.25*C = $372.50                      Now we get the variable alone:

$0.25* C = $56.50                                Lastly we need to divide both sides by $0.25:

C = 226

 

Now we can plug this into the equation we solved for A:

A = 429 - C

A = 429 - 226

A = 203

 

So the number of adults is 203 and the number of children is 226.

 

We can check this by plugging these numbers into the second equation

$1*A + $0.75*C = $372.50

$1*203 + $0.75*226 = $372.50

$203 + $169.5 = $372.50

$372.50 = $372.50

Answer 2

There are two unknowns in this problem, the number of children and the number of adults. Let us denote the number of children "c" and adults "a". We know:

 

1. a + c = 429   <--- This represents the total people at Bingo Night
2. 1.00a + 0.75c = 372.50   <--- This represents the total receipts from the children and adults attending

From equation 1. we know:

 

• a = 429 - c

 

We substitute this into equation 2. to find:

 

• 1.00(429 - c) + 0.75c = 372.50
• 429 - c + 0.75c = 372.50
• 429 - 0.25c = 372.50
• -0.25c = -56.50
• c = 226

 

We can know substitute 226 back into equation 1. and find that there were 203 adults and 226 children at Bingo Night.