Question

System word problems 4. Ms. Hoffman tells you that your next test is worth 33 points and has 9 problems on it. Multiple-choice questions are worth 2 points each and word problems are worth 5 points each? How many word problems will be on the test and how many multiple - choice questions will be on the test? Define Variables:System of Equations:Answer as a sentence:

Answer 1

Case: Word Problems (leading to simultaneous equation)

Given: A test case with number of problems and number of points

Required: To find how many word problems and how many multiple -choice questions are on the test

Method:

Defining variables

Let the number number of word problem questions be represented by w

Let the number number of multiple-choice questions be represented by m

Forming equations

Number of problems

m + w = 9...........(1)

Number of points

2 points per m

5 points per w

2m + 5w = 33.......(2)

Solving simultaneously

System of equations:

`\begin{gathered} m+w=9\ldots\ldots\text{.}\mathrm{}(1) \\ 2m+5w=33\ldots\text{.}\mathrm{}(2) \\ \text{Making m subject} \\ m=\text{ 9-w} \\ \text{Plug m as 9-w in equation (2)} \\ 2m+5w=33 \\ 2(\text{9-w})+5w=33 \\ 18\text{ - 2w +5w = 33 } \\ 18\text{ + 3w = 33} \\ 3w\text{ = 33-18} \\ 3w\text{ = 15} \\ \text{Dividing both sides by 3} \\ w\text{ = 5.} \\ \\ \text{Plug w=5 in equation (1)} \\ m+w=9 \\ m+5=9 \\ m\text{ = 9 -5} \\ m=4 \end{gathered}`

Final answer:

Answer as a sentence

There are a total of 4 multiple-choice questions AND

a total of 5 word problem questions