ACT Math Question

<p>This is probably a really easy problem, but I honestly dont know how to get the answer. I feel really bad because I am in AP Cal AB and I can't do this Alegbra problem.</p>

<p>To increase the mean of 4 numbers by 2, by how much would the sum of the 4 numbers have to increase?</p>

<p>F. 2
G. 4
H. 6
J. 8</p>

<p>The answer is J, but I dont know what work has to be done to solve the problem. Please Help Me!!!! :)</p>

<p>I need help with this problem as well.</p>

<p>Meg pounded a stake into the ground. When she attached a leash to both the stake and her dog's collar, the dog could reach 9 feet from the stake in any direction. Using 3.14 for pi, what is the approximate area of the lawn, in square feet, the dog could reach from the stake?</p>

<p>The answer is 254.</p>

<ol>
<li><p>The way I solve the average problems is to multiply the average by the number of values. If you want to increase the values by 2, multiply 2 by the number of values (4) and you get 8. </p></li>
<li><p>The phrase "When she attached a leash to both the stake and her dog's collar, the dog could reach 9 feet from the stake in any direction" really is just a fancy way of telling you the radius is 9 feet. Knowing the radius, we can substitute that into the formula for the area of a circle (area ~ 3.14*r^2).
So,
(9^2)(3.14) = 254.34 --> 254</p></li>
</ol>

<p>Hope that helps! I'm in Calc too, so I had to go back and review everything :(</p>

<p>Another way to look at 1:</p>

<p>The mean (call it M) of the original four numbers is just their sum (call it S) divided by 4. In other words, S/4=M. The question can be expressed as (S+x)/4=M+2, where x is what you are trying to find. Since M=S/4, then by substitution, (S+x)/4=(S/4)+(x/4)=M+2=(S/4)+2. Subtract S/4 from both sides and you have x/4=2, or x=8.</p>

<p>Thank You,</p>

<p>I actually tried to use "2 times pi times r" for the first problem and I think that is the formula for the circumference of a circle.</p>

<p>I totally understand the second problem now, so again Thank You.</p>

<p>This is how I would tackle these problems:</p>

<p>1) mean = sum / 4</p>

<p>We want to increase the mean by 2:</p>

<p>mean + 2 = sum / 4 + 2 = sum / 4 + 8/4 = (sum + 8)/4</p>

<p>Thus, the sum must increase by 8.</p>

<p>2) We have a circle of radius 9 feet. Since A = Pi<em>r^2, the area of this circle therefore is Pi</em>(9)^2 = 81Pi. If we let Pi = 3.14, then we get</p>

<p>81(3.14) = 254.34.</p>

<p>The trick to doing these problems is to realize that, since the time given to you is so little, there must be a simple way of getting it. The problem cannot involve complicated algebraic manipulations because there's not time for such things. Therefore, a good strategy is to write down anything that seems obvious from the problem in the form of an equation and see what you can do with it. Often times, there's only one thing that can be done; in these cases, it's almost certain that this will yield you the answer.</p>

<p>Thx for the tip.</p>