Question

mid-lesson checkpoint
the cost of an adult ticket and 2 child tickets at an amusement park is $55. if x represents the cost of a child ticket and y represents the cost of an adult ticket, write an equation that models this situation.
graph your equation on the set of axes below.
if an adult ticket costs $25, how much does a child ticket cost? justify your answer using the graph.
feedback: how confident are you in comparing and ordering rational numbers? circle your answer.
i totally get it! i feel ok, but could use some more practice. i dont get it. i need help.

Explanation:

Step1: Write the equation

The cost of an adult ticket (\(y\)) and 2 child tickets (\(2x\)) is $55. So the equation is \(y + 2x=55\).

Step2: Solve for \(x\) when \(y = 25\)

Substitute \(y = 25\) into the equation \(y+2x = 55\).
We get \(25+2x=55\).
Subtract 25 from both sides: \(2x=55 - 25\).
\(2x=30\).
Divide both sides by 2: \(x = 15\).

To graph \(y+2x=55\) (or \(y=-2x + 55\)), we can find two points.
When \(x = 0\), \(y=55\) (the \(y\)-intercept).
When \(y = 0\), \(0=-2x+55\), then \(2x=55\), \(x = 27.5\). Plot the points \((0,55)\) and \((27.5,0)\) and draw a straight - line through them. When \(y = 25\), on the graph, we find the corresponding \(x\) - value.

Answer:

The equation is \(y + 2x=55\). A child ticket costs $15.