Answer to Question #92153 in Algebra for Kina

Question

1000 people entered a math contest to see how many questions out of 20 they could answer correctly in 5 minutes. 15% of them answered 12 correct, 3/5 answered 15 correct and the rest answered 18 correct. What was the percentage correct everyone earned?

Answer 1

So

Let us define the general number of questions that were given to participants(taking in account the questions of every single person)by multiplying the quantity of participants by the number of questions given for each:

$$General.questions.number=1000×20$$

Then,we are supposed to determine the number of people in each group.

$$N_1=1000×0.15$$ $$N_1=150$$

$$N_2=1000×\frac{3}{5}$$

$$N_2=600$$

$$N_3=N-(N_1-N_2)$$

$$N_3=250$$

Once we've done this, we have to detect the general number of questions that were answered correctly by detecting the quantity of questions that were answered correctly in each group and adding them all together.

$$Q_1=12×N_1$$ $$Q_1=1800$$ $$Q_2=15×N_2$$ $$Q_2=9000$$ $$Q_3=18×N_3$$

$$Q_3=4500$$

$$Q=Q_1+Q_2+Q_3$$ $$Q=15300$$

And to define the percentage we need the general number of questions answered accurately divide by the general number of questions:

$$P=\frac{Q}{N}×100\%$$ $$P=76.5\%$$

Answer:

$$P=76.5\%$$