Question

The average of five numbers is 10. If one of the numbers is multiplied by 3, the average of the numbers increases to 14. Which of the five numbers is multiplied by 3?

Answer 1

Let the five numbers be
`a,b,c,d,e,` so
`(a+b+c+d+e)/(5)=10\implies a+b+c+d+e=50.` Suppose we multiply
`a` by 3, so
`3a+b+c+d+e=5\cdot 14=70.` Subtract the first equation from this equation to get
`2a=20\implies a=10,` so
`\boxed{10}` is the number that is multiplied by 3.