This exam was adminstered in January 2024 .

### June 2024 Algebra, Part IV

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

**35.** * Courtney went to a coffee shop to purchase lattes and donuts for her friends. One day she
spent a total of $15.50 on four lattes and two donuts. The next day she spent a total of $18.10 on
three lattes and five donuts. All prices included tax.
*

*If x represents the cost of one latte and y represents the cost of one donut, write a system of
equations that can be used to model this situation.
*

*Courtney thinks that one latte costs $2.75 and one donut costs $2.25.
Is Courtney correct? Justify your answer.
*

*Use your equations to determine algebraically the exact cost of one latte and the exact cost of
one donut.
*

**Answer: **

Answer every section of this question to get full credit. if you make a mistake on top, you will not be penalized more than once if you are consistent until the end and give a final answer. Make sure you use

**x**and

**y**and not

*L*and

*D*because the questions says to use x and y!

You should be able to read the first two sentences and translate them into equations.

4x + 2y = 15.50

3x + 5y = 18.10

Two find out if Courtney is correct, you only have to substitute those values into BOTH equations to see if those values make BOTH equations true.

4(2.75) + 2(2.25) = 15.50 (check)

3(2.75) + 5(2.25) = 19.50 =/= 18.10 (does not check!)

Courtney is incorrect.

Finally, copy your system of equations and solve through elimination. Note that it says algebraically, so you won't get full credit for graphing the equations in your calculator and finding the intersection point.

4x + 2y = 15.50

3x + 5y = 18.10

12x + 6y = 46.50

12x + 20y = 72.40

14y = 25.90

y = $1.85

The price of one donut is $1.85. If you got an repeating decimal, or anything that doesn't come out to an exact number of dollars and cents, that should tell you that there was an error somewhere. The problem deals with money and must have a monetary answer.

Now that you know the price of a donut, you can find the price of a latte by using either of the original equations:

4x + 2y = 15.50

4x + 2(1.85) = 15.50

4x + 3.70 = 15.50

4x = 11.80

x = 2.95.

The price of a latte is $2.95.

**End of exam**

How did you do?

Questions, comments and corrections welcome.

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