Respuesta :
SOLUTION:
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:
[tex]\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}[/tex]Final answer:
Answer as a sentence
There are a total of 4 multiple-choice questions AND
a total of 5 word problem questions
