<p>I was working on PR SAT math questions and found some interesting questions. However, I couldn't solve them for some reason....</p>
<ol>
<li><p>In Miss Hoover's class, the ratio of boys to girls is x to y. If the total number of children in the class is five times the number of boys in the class, which of the following is an expression for the number of girls in the class, in terms of x and y?</p></li>
<li><p>A 50-foot wire runs from the roof of a building to the top of a 10-foot pole 14 feet across the street. How much taller would the pole have to be if the street were 16 feet wider and the wire remained the same length?</p></li>
</ol>
<ol>
<li>ratio of boys to girls is x to y.
which means total students = x+y.
so.
x+y(total students) = 5x(5 times the number of boys)
x+y=5x
y=4x <----subtract 1x from both sides.</li>
</ol>
<p>btw^^y=(number of girls)</p>
<ol>
<li>pole would have to be 40 ft.
easier to explain with picture</li>
</ol>
<p>just think about a triangle and use reverse pythagorean thereom.</p>
<p>c^2 = a^2 + b^2</p>
<p>c is 50 (length of rope)
a is 30 (16 added to original 14 foot street)
b is what you are looking for</p>
<p>so plug them in the above equation</p>
<p>50^2 = 30^2+b^2</p>
<p>2500 = 900 +b^2</p>
<p>1600 = b^2
40=b</p>
<p>which is 30 feet more than the original 10. don’t get fooled by the problem and write 40 since it asks *how much taller the pole would have to be *=)</p>
<p>good luck mate =P</p>
<p>^Actually, that doesn’t make any sense at all if you think about it.</p>
<p>Using Pythagorean theorem with 50 and 14 yields 48, which is the vertical distance from the top of the pole to the top of the building. So the building is 58 feet tall.</p>
<p>Using Pythagorean theorem with 50 and 30 yields 40, which is the vertical distance from the top of the new pole to the top of the building. So the new pole is 18 feet tall, which is 8 feet more than the original.</p>
<p>the answer for first Q is (5xy)/(x+y), and the answer for second Q is 8ft. I still don’t understand the reason though… How can the pole get taller?</p>
<p>Well think about it this way Legend. If the length of rope is constant, and the distance from the building to the pole is increased, then one of two things can happen. Either the pole can increase in height, or it can decrease. It can’t remain the same, because when one variable stays constant and another changes, the third variable cannot remain the same. I’m not sure if that made any sense, so let me continue.</p>
<p>If the distance between the pole and building increases, then the pole will have to rise since the rope isn’t compensating for the widening of the road. </p>
<p>If I could send you a picture it would make perfect sense, sorry I epicly failed in trying to explain that problem lol.</p>