# Math questions

<p>Amanda travel to work from home in 60 minutes. If,on her way home,she
increases her average speed by 20 % and she travel by the exact same route,
how many minutes will it take her to get home ?</p>

<p>1)48
2)50
3)54
4)60
5)64</p>

<p>A jar contains five marbles,five of which are white
and the rest black. What is the least number of white marbles
that must be added to the jary so that least three-fifths of the marbles
will be white?</p>

<p>If x and y are positve integers such that x^2 + y^2 = 41,then what is the value of (x + y)^2?
I knew by brute-forcing that 4^2 + 5^2 = 41,but is there mathmatical way to tackle this problem!?</p>

<p>In one basketball game, Tamara made 50 % of her shots,and in the two games,she made 60% of her shots.
In the two games,she made 52 % of her shots altogether. If she took a shots in the first game and b shots in the second game, what is the value of a/b?</p>

<p>Amanda travel to work from home in 60 minutes. If,on her way home,she
increases her average speed by 20 % and she travel by the exact same route,
how many minutes will it take her to get home ?</p>

<p>1)48
2)50
3)54
4)60
5)64</p>

<p>*okay. Put "P/60" as your per-minute speed. Take "P" as the symbol for the total distance between work and home. Now, the new speed should be increased by 20%, so times "P/60" by "1.2." You get 0.02P.
Since this is your new speed and you want to get the time it takes, you should divide the distance P by the new speed 0.02P. You'll get 50 minutes after reversing 0.02. The answer is 2.</p>

<p>A jar contains five marbles,five of which are white
and the rest black. What is the least number of white marbles
that must be added to the jary so that least three-fifths of the marbles
will be white?</p>

<p>*I don't understand. Five marbles in total??</p>

<p>If x and y are positve integers such that x^2 + y^2 = 41,then what is the value of (x + y)^2?
I knew by brute-forcing that 4^2 + 5^2 = 41,but is there mathmatical way to tackle this problem!?</p>

<p>*For this type of problem, you can't get a logical method. x+y squared x^2+2xy+y^2, and there is no way you can get the value of 2xy from the provided info. Just do your best in guessing !</p>

<p>In one basketball game, Tamara made 50 % of her shots,and in the two games,she made 60% of her shots.
In the two games,she made 52 % of her shots altogether. If she took a shots in the first game and b shots in the second game, what is the value of a/b?</p>

<p>*The shots you made in the first game is represented as .5a, because you have to times the percentage by "a" (the total no. of shots). Do the same for the second game and you'll get .6b.
(.5a+.6b) should be put over (a+b), which is the total no. of shots for both games. This fraction, (.5a+.6b)/(a+b), should equal 52%, or .52. Cross-multiply.
You'll get an equation like this: 2a=8b, in other words, a=4b.</p>

<p>Replace a with 4b in the a/b formula. You'll get 4. The answer is 4.</p>

<p>I hope this helped you! :)</p>

<p>1) The answer is 2. The fastest way to do this is to realize speed and time are inversely proportional. More speed = less time.</p>

<p>Thus, if Amanda increases her speed by 20%, then her travel time must be less than 60 minutes. That eliminates choices 4 and 5. </p>

<p>Amanda's new speed is 1.2x her original. Set up an equation to find her new speed:</p>

<p>1.2x = 60
60/1.2 = 50. </p>

<hr>

<p>2) Here is the correct problem statement:</p>

<p>A jar contains 15 marbles, five of which are white and the rest black. What is the least number of white marbles that must be added to the jar so that 3/5ths of the marbles will be white.</p>

<p>Set up a proportion:</p>

<p>5+x/15+x = 3/5
where x = number of white marbles you'll be adding</p>

<hr>

<p>3) Absolutely, there is a mathematical way to crack this problem.</p>

<p>(x+y)^2 = x^2 + 2xy + y^2 </p>

<p>x^2 + y^2 = 41 </p>

<p>(x+y)^2 = 41 + 2xy</p>

<p>@IceQube,
You said
"3) Absolutely, there is a mathematical way to crack this problem.</p>

<p>(x+y)^2 = x^2 + 2xy + y^2 </p>

<p>x^2 + y^2 = 41 </p>

<p>(x+y)^2 = 41 + 2xy "
But how can you get the answer to (x+y)^2? From what I understand, there's no other way than just guessing that either x or y is 4 and the other is 5, thus the answer is 81.</p>

<p>You have some things that average 50, others that average 60 but together they average 52. This is a theme that comes up now and again and it is worth thinking about and understanding the quicker way. </p>

<p>KEY IDEA: For a bunch of numbers to have a certain average, the value of the "surplus" contributed by numbers higher than the average has to be balanced by the value of the "deficit" contributed by numbers lower than the average.</p>

<p>Really think about that because once you understand it, it offers a quick path to the solution.</p>

<p>In this case, the final average is 52. The 50's are all going to contribute a deficit of 2 each. The 60's are going to contribute a surplus of 8 each. How can the deficits balance the surpluses? There must be 4 times as many 50's as 60's (b/c 2x4=8). So a/b = 4</p>

<p>Thanks guys.</p>