Respuesta :
Answer:
3-point questions = 7
4-point questions = 11
5-point questions = 7
Step-by-step explanation:
Let x, y and z be number of 3-point, 4-point and 5-point questions respectively.
We are told that number of total questions in the quiz is 25.
[tex]x+y+z=25...(1)[/tex]
We are also told that number of 3-point questions is 4 less than the number of 4-point questions.
[tex]y=x+4...(2)[/tex]
The quiz is worth 100 points.
[tex]3x+4y+5z=100...(3)[/tex]
Substituting equation 2 in equation 1 we will get,
[tex]x+x+4+z=25[/tex]
[tex]2x+z=25-4[/tex]
[tex]z=21-2x[/tex]
Upon substituting value of y and z in equation 3 we will get,
[tex]3x+4(x+4)+5(21-2x)=100[/tex]
[tex]3x+4x+16+105-10x=100[/tex]
[tex]7x+121-10x=100[/tex]
[tex]7x-10x=100-121[/tex]
[tex]-3x=-21[/tex]
[tex]x=\frac{21}{3} =7[/tex]
Therefore, number of 3-point questions is 7.
Now we will find y by substituting x=7 in equation 2.
[tex]y=7+4=11[/tex]
Therefore, number of 4-point questions will be 11.
Now we will substitute value of x and y in equation 1 to find our z.
[tex]7+11+z=25[/tex]
[tex]18+z=25[/tex]
[tex]z=25-18=7[/tex]
Therefore, number of 5-point questions is 7.
