Question

1. A student took 60 minutes to answer a combination of 20 multiple-choice and extended-response questions. She took 2 minutes to answer each multiple-choice question and 6 minutes to answer each extended-response question.
a. Write a system of equations to model the relationship between the number of multiple-choice questions (m) and the number of extended-response questions (r).


b. How many of each type of question was on the test? Show your work.


2. A scientist wants to make 6 milliliters of a 30% sulfuric acid solution. The solution is to be made from a combination of 20% sulfuric acid solution and a 50% sulfuric acid solution. (Review "Mixture Problems Resources" for help.)


a. Write a system of equations to model the relationship.


b. How many milliliters of each solution must be combined to make the 30% solution? Show your work.


3. Choose the method of solving (graphing, substitution, elimination) that seems easier to use for the system below. Explain why you made your choice. You do not need to solve the system.


2x-3y=4

2x-5y=-6

Answer 1

Answer:

1) m=15 and r =5

2) 4 and 2 ml

3) x= 0.5 and y = -1

Step-by-step explanation:

given that m multiple choice questions and r extended response questions.

Also given that a) m+r = total no of questions =20 ... i and

                        2m+6r = total time taken = 60  ... ii

b) Divide second equation by 2, m+3r = 30  ... iii

                                                  m+r  = 20   ... i

Subtract to get 2r =10 or r =5

m = 20-5 = 15

Verify: m+r = 15+5 =20

and     2m+6r = 30+30 = 60 minutes.  

Hence verified

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2) Let a litres of 20% solution and b litres of 50% solution be mixed

a) Then total volume = 6 ml = a+b  ... i

Resulting solution = 30% of 6 ml = 1.8 = 0.2a+0.5b ... ii

b) Solve i and ii

b = 6-a: substitute in ii.

0.2a + 3-0.5a = 1.8

Or a = 4 ml and b = 2ml

Verify: Total volume = a+b =6ml and

concentration = 0.2(4)+0.5(2) = 1.8 = 30% of 6 ml.

Thus verified

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3) 2x-3y=4 ...i

  2x-5y =6... ii

Because x term has the same coefficient in both the equations, elimination is easier.

i-ii gives 2y =-2 or y =-1

Substitute in i, 2x+3 =4 or x = 0.5

So answer is x = 0.5 and y =1