The heights of four of the starting players on the basketball team are 183 cm, 178 cm, 174 cm, and 185 cm. If the mean height of all five starting player is 182 cm, what is the height of the fifth starting player?
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To find the height of the fifth starting player, we can use the formula for the mean (average) of a set of numbers.
The mean height of all five starting players is given as 182 cm. We are given the heights of four of the players: 183 cm, 178 cm, 174 cm, and 185 cm.
To find the sum of all five heights, we can add these four heights to the height of the fifth player and then divide by 5 (the total number of players):
(183 cm + 178 cm + 174 cm + 185 cm + x cm)/5 = 182 cm
We need to solve this equation for x, which represents the height of the fifth player.
First, we can simplify the equation by multiplying both sides by 5:
183 cm + 178 cm + 174 cm + 185 cm + x cm = 5 * 182 cm
Now, we can combine like terms on the left side:
720 cm + x cm = 910 cm
Next, we can isolate x by subtracting 720 cm from both sides:
x cm = 910 cm - 720 cm
Simplifying further:
x cm = 190 cm
Therefore, the height of the fifth starting player is 190 cm.