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

Question

2 years ago

7

of $1221.80. How many adult
tickets were sold that day?

1 answer:

Tju [1.3M] · Answer 1 · 2023-11-04T09:04:57+03:00

<h2>Systems of Equations</h2>

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

<h2>Solving the Question</h2>

Let <em>a</em> represent the number of child tickets.

Let <em>b</em> represent the number of adult tickets.

We're given:

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:

$a+b=163$

$6.2a+9.4b=1221.8$

<h3>Solving the System of Equations</h3>

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 <em>a</em>:

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

Solve for <em>b</em>:

$b=66$

Therefore, the number of adult tickets sold is 66.

<h2>Answer</h2>

66