<p>If y varies directly as x, and if y = 8 when x = a, and y = 12 when x = a + 10, what is the value of a?</p>
<p>I'd love to know how to solve this for tomorrow xD</p>
<p>Thanks in advance for help :D</p>
<p>I thought I knew how but I ended up screwing up, maybe you can figure out where?</p>
<p>If y varies directly as x, then y=kx, where k is some constant. </p>
<p>since y=8 when x=a, then 8=ka</p>
<p>since y=12 when x=a+10, then 12= k(a+10)</p>
<p>To find the constant, we first solve for a:</p>
<p>12= ka +10k</p>
<p>-ka=-12+10 k Divide by -k:</p>
<p>a= -12/k-10</p>
<p>Now substitute the constant into the first equation:</p>
<p>8=(-12/k-10)k</p>
<p>8= -12-10k</p>
<p>20= -10k</p>
<p>-2= k , so the constant is -2. Now substitute -2 for k in both equations to find a. </p>
<p>8= a(-2), so a= -4. Check w/ the other equation:</p>
<p>12=(-4+10)(-2)
-12=12</p>
<p>^^ NOOOOOOOOOOOO haha damn</p>
<p>GOT IT! haha. set it up the same way:</p>
<p>8= ak and
12= (a+10)k </p>
<p>Solve for a: a= 8/k</p>
<p>Substitute:
12= (8/k)k+ 10k
12= 8 + 10k
4= 10k
k = 2/5</p>
<p>SO</p>
<p>8= a(2/5)
a= 20</p>
<p>check w/ other</p>
<p>12= ak +10k
12= 8 +4</p>
<p>Use proportions</p>
<p>a : 8 :: (a + 10) : 12</p>
<p>Solving for a</p>
<p>a / 8 = (a + 10 ) / 12</p>
<p>12a = 8a + 80</p>
<p>4a = 80</p>
<p>a = 20</p>
<p>I got the same thing.</p>
<p>y = kx </p>
<p>8 = ka
12 = ka+k10</p>
<p>-R1+R2 -> R2</p>
<p>4 = 10K</p>
<p>2/5 = K</p>
<p>12 = 2/5(a+10)</p>
<p>30-10 = a
20 = a</p>
<p>8 = (2/5)(20)
8=8</p>
<p>12 = (2/5)(10+20)
12 = (2/5)(30)
12=12</p>