What height is the substitute player?

Question

A 5 a side football team has an average height of 1.82 meters, but when their substitute is included the team's average height increases by 2cm.

What height is the substitute player?

help!!

Answer 1

HINT: He virtually adds 2 cm to every member of the previous team.

Answer 2

What is the total height of the five players? What is the total height of the six players? Subtract.

Answer 3

When you ask a question on Math.SE, please always state the work you have done on the problem, so we feel more inclined to help you knowing you've made an effort. I'm feeling generous today, so I'll walk you through this one, but please heed my advice in future.

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The average team member's height is $1.82m$. There are $5$ of them, so the team's total height is $5*1.82m=9.1m$

When the substitute is added in, the average is $1.82m+0.02m=1.84m$. There are now $6$ players, so the total height is $6*1.84=11.04m$

The answer you require is the height of the sixth player, so this is $11.04m-9.1m=1.94m$

Answer 4

Let the heights of the five regular players on the team be $a_1,a_2,a_3,a_4,a_5$ respectively. Let the height of the substitute player be $x$.

We are told two major pieces of information:

"The average height of the five regular players on the team is $1.82$ meters."

This sentence can be translated into mathematical symbols as the following:

$$\frac{a_1+a_2+a_3+a_4+a_5}{5}=1.82~m$$

"The average height of all six players (the five regular players as well as the substitute player) is two centimeters more than the average height of the five regular players"

This sentence can be translated into mathematical symbols as the following:

$$\frac{a_1+a_2+a_3+a_4+a_5+x}{6}=1.84~m$$

From here you can rearrange the equations a bit and combine them in order to isolate $x$ by itself, for example via substitution or via elimination.

Six times the second equation minus five times the first equation.

Note: There is not enough information to uniquely determine $a_1$ or $a_2$, etc... but there is enough information to conclude $a_1+a_2+a_3+a_4+a_5$ and therefore $x$ as well.