Question

On a certain IQ test, eleven people averaged a 101.5. A certain reality TV star took

Answer 1

Answer:

59.98

Step-by-step explanation:

To find the average of a set of numbers, we sum them all together and divide them by the size of the set. Here, we start out with 11 IQ scores. We don't know what they are, but we can still set up an equation with the information we do have. Let's call the sum of those 11 score s. The average must be s/11, which we know is 101.5. With that, we can set up and solve and equation for s:

$\dfrac{s}{11}=101.5\\s=101.5(11)\\s=1116.5$

Let's call the score of the reality TV star r. If we add their score to the set, we now have 12 scores. The sum of those scores is gonna be the sum of the previous scores, 1116.5, plus the reality TV star's score, r. To find the average, we divide the sum by 12. Finally, we're told that this average is exactly 98.04. Putting all of this into an equation gives us

$\dfrac{1116.5+r}{12}=98.04$

We can now solve for r algebraically, first by multiplying both sides by 12:

$1116.5+r=98.04(12)\\1116.5+r=1176.48$

And then subtracting 1116.5 from both sides:

$r=1176.48-1116.5\\r=59.98$