An instructor wants to write a test with 25 questions where each question is worth 3, 4, or 5 points based on difficulty. he wants the number of 3-point questions to be 4 less than the number of 4-point questions, and he wants the quiz to be worth a total of 100 points. how many 3, 4, and 5 point questions are there?

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.

We are also told that number of 3-point questions is 4 less than the number of 4-point questions.

The quiz is worth 100 points.

Substituting equation 2 in equation 1 we will get,

Upon substituting value of y and z in equation 3 we will get,

Therefore, number of 3-point questions is 7.

Now we will find y by substituting x=7 in equation 2.

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.

Therefore, number of 5-point questions is 7.  

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get