Question

the average weight of 6 people is 173, a 7th person gets on and now the average weight is 165, how much did the 7th person weigh

Answer 1

Answer:

The 7th person weighted 117

Step-by-step explanation:

Average Value

The mean or average of a number n of measurements is defined as the sum of all values divided by n.

$\displaystyle \bar x=\frac{\sum x_i}{n}$

The question gives us some input data. The average weight of n=6 people is $\bar x=173$. With this information, we can set this relationship:

$\displaystyle 173=\frac{\sum x_i}{6}$

From the above equation, we know the sum of the first 6 persons:

$\sum x_i=6*173=1,038$

When a 7th person gets on, the new average gets down to 165 and n=7. The equation for the new average is:

$\displaystyle 165=\frac{\sum x_i+X}{7}$

Note we have a new summand to the numerator. It's the weight of the 7th person. Let's solve for X:

$\displaystyle 165=\frac{1,038+X}{7}$

Multiply by 7:

$7*165=1,038+X$

Operate and swap sides:

$1,038 +X=1,155$

$X=1,155-1,038=117$

The 7th person weighted 117

Answer 2

Answer:

117

Step-by-step explanation:

The average of all 7 people is the total weight of the original 6 people, plus the weight of the 7th person, all divided by 7.

For problems like this involving an average of numbers that are "close" together, here is a different strategy for solving the problem that you might like to try.

The original 6 people have an average weight of 173, which is 8 pounds more than the average of all 7 people. So all together, the weight of those 6 people is 6*8=48 pounds over the 165 average. That means the 7th person's weight must be 48 pounds below the 165 average.

So the weight of the 7th person is 165-48 = 117 pounds.