  3 math questions

<p>1) If a:b = 3:5 and a:c = 5:7, what is the value of b:c?</p>

<p>(A) 3:7
(B) 21:35
(C) 21:25
(E) 7:3</p>

<p>2) If 500 pounds of mush will feed 20 pigs for a week, for how many days will 200 pounds of mush feed 14 pigs?</p>

(B) 5
(C) 6
(D) 7
(E) 8</p>

<p>3) If 3a=2b and 3b=5c, what is the ratio of a to c?</p>

<p>Can someone explain these?</p>

<p>1) Since it's a:b and a:c, make a the same number for each ratio, which would be 15... 15:25 and 15:21. B:C would be 25:21.</p>

<p>2) No idea. :/</p>

<p>3) I don't understand why it's 10:9 actually.. I kept getting 9:10... Someone else explain? o.O</p>

<p>1- b/c= (a/c)/(a/b)= (a/c)<em>(b/a)=b/c
therefore b/c=(5/7)/(3/5)=(5/7)</em>5/3=25/21</p>

<p>2- 500 pounds feed 20<em>7=140 pig days
thus 500 pounds can feed 14 pigs for 10 days
Therefore 200 pounds will feed 14 pigs for 10</em>200/500= 4 days</p>

<p>3- 3a=2b -> b=3a/2
substitute in 3b=5c: 3*3a/2=5c ->9a/10=c
a/c=10/9</p>

<p>Thank you very much guys.</p>

<p>But could someone explain number 3 again? I keep getting 9/10, i do not see why we get its reciprocal.</p>

<p>Sure
I just go with the algebra here is answer for number 1)</p>

<p>1)</p>

<p>(a / b) / ( a / c) = (a / b) * (c / a) = 1/b * c/1 = c/b then inverse</p>

<p>3:5 * 7 / 5 = 21 / 25 = 25 / 21;</p>

<p>3a = 2b;
b = 3a/2;</p>

<p>3b = 5c = 3(3a/2) = 5c;</p>

<p>9a/2 = 5c;</p>

<p>9a = 10c;</p>

<p>9a / a = 10c / a;</p>

<p>1/10* 9 = 10c/a * 1/10;</p>

<p>9/10 = c/a ,then inverse to get a/c = 10/9;</p>

<p>Just follow the algebra it will solve these questions really easy for you or you can play with the equation and see how will affect the outcome.</p>

<p>For questions like 1, and 2: Plug-in numbers. It'll make it a whole lot easier, if you're particularly messy with algebra.</p>

<p>If 3a=2b and 3b=5c, what is the ratio of a to c?</p>

<p>Let c = 2</p>

<p>Therefore, 5(2) = 3(3.333)
In which case, 2(3.333) = 3(2.333)</p>

<p>What's the ratio between 2.333 and 2? Put it on your calculator. The answer is 10/9.</p>