What was the average score for these eleven students together?

Question

The whole question:

The average of four students' scores on a test was 70. The sum of seven other students' scores on the same math test was 160. What was the average score for these eleven students together?

 

I thought that I add 4(70) and 7(160) and divide by 11, but it seems that it is incorrect. Please help. Thank you.

Answer 1

(x₁ + x₂ + x₃ + x₄) / 4 = 70

 

x₁ + x₂ + x₃ + x₄ = 280

 

 

  

The first 4 students' scores add up to 280.

The other 7 students' scores add up to 160.

 

If we take the total sum of scores and divide it by the total number of people who took the test, we will have a combined average.

 

Total average = (280 + 160) / 11

                     = 440 / 11

                     = 40

Answer 2

We have the first 4 students scores averaged 70...

(A+B+C+D)/4 = 70

A+B+C+D = 280

 

The sum of the first 4 students grades was 280

The sum of the other 7 students grades was 160

 

To find the overall average (280+160)/11 = 440/11 = 40

 

Note that for the last 7 students their average was 160/7 = 22.86 or ≅ 23

That is why the 11 overall had such a low average