<p>This was a math question on an old PSAT (2005).</p>
<p>Question: If x^10 = 5555 and x^9/y = 5, what is the value of xy??</p>
<p>Answer: 1111</p>
<p>Could someone tell me how you get 1111??</p>
<p>Thanks in advance</p>
<p>well x^9/y=5</p>
<p>and x^10=5555</p>
<p>so divide x^9/y by x^10.</p>
<p>you get 1/xy=1/1111</p>
<p>x^10=5555
x=5555^(1/10)</p>
<p>x^9/y=5
x^9/5=y
y=(5555^(1/10))^9/5
y=(5555^(9/10))/5</p>
<p>5555^(1/10)*(5555^(9/10))/5
5555^((1+9)/10)/5
5555^(10/10)/5
5555^(1)/5
5555/5
1111</p>
<p>x^10 = 5555</p>
<p>x^9/y= 5</p>
<p>xy = ? </p>
<p>Now, take x^9/y = 5 and multiply both sides by y to get x^9 = 5y</p>
<p>then, divide both sides of x^10 = 5555 by x to get x^9 = 5555/x </p>
<p>so now you know that 5y = 5555/x so multiply both sides by x to get 5xy=5555 and then divide by 5 to get xy = 1111</p>
<p>Edit: Wow ccers are fast. lol i think my explanation is the best :D</p>
<p>Thanks guys. I get it now. And yes, hpa10’s way is much easier.</p>
<p>I think this is the easiest and fastest way to do it:</p>
<p>First you have to make the observation that:
x^9 * xy = x^10</p>
<p>So then you substitute with what was given:
5 * xy = 5555</p>
<p>Solve for xy
xy = 1111</p>