Question

At the city museum, child admission is $6.20 and adult admission is $9.40. On Thursday, 163 tickets were sold for a total sales of $1221.80. How many adult
tickets were sold that day?

Answer 1

Systems of Equations

To form a system of equation from a word problem, we must recognize different variables to form different equations.

Solving the Question

Let a represent the number of child tickets.

Let b represent the number of adult tickets.

We're given:

• 1a = $6.20
• 1b = $9.40
• a and b in total is 163
• Total sales = $1221.80

Because we're given that a and b in total is 163, we can form the following equation:

$a+b=163$

We're also given that the total sales made is $1221.80. Because we know that 1a = $6.20 and 1b = $9.40, we can also form the following equation:

$6.2a+9.4b=1221.8$

Here are our two equations:

$a+b=163$

$6.2a+9.4b=1221.8$

Solving the System of Equations

We can solve using the method of elimination. Multiply both sides by 6.2 in the first equation:

$6.2(a+b)=6.2(163)\\6.2a+6.2b=1010.6$

Subtract this new equation from the second equation to cancel out a:

$\hspace{10}6.2a+9.4b=1221.8\\- 6.2a+6.2b=1010.6\\\rule{100}{0.5}\\3.2b=211.2$

Solve for b:

$b=66$

Therefore, the number of adult tickets sold is 66.

Answer

66