Algebra Problems of the Day (Algebra Regents, January 2025 Part IV)

This exam was adminstered in January 2025.

January 2025 Algebra, Part IV

A correct answer is worth up to 6 credits. Partial credit can be given. Work must be shown or explained.

35. Anna plans to spend $30 on balloons and party hats for her daughter’s birthday party. Including tax, balloons cost $2 each and party hats cost $1.50 each. The number of party hats Anna needs is twice as many as the number of balloons.

If x represents the number of balloons and y represents the number of party hats, write a system of equations that can be used to represent this situation.

Graph your system of equations on the set of axes below.

State the coordinates of the point of intersection of your lines.

Explain what each coordinate means in the context of the problem.

Answer:

Write the system of equations for the number of balloons and hats and for the price of the balloons and hats. Then rewrite them solving for y in terms of x (isolate the y variable) so you can put them into your graphing calculator or graph using the slope and intercept.

This question may be confusing to anyone who did a lot of test prep because it seems like it should be an inequality question, but it is NOT.

y = 2x
2x + 1.50y = 30

1.5y = -2x + 30
y = -4/3x + 20

The graph would look as follows:

The coordinates of the solution are (6,12).

In the context of the problem, there will be 12 hats and 6 balloons.

End of Part Exam

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