<p>In 1980, Judy was 3 times as old as Adam, but in 184 she was only twice as old as he was. How old was Adam in 1994?</p>
<p>If a = Adam’s age in 1980, then in 1980 j = 3a.</p>
<p>In 1984, Adam’s age was (a+4). Judy’s age was (3a+4), but her age was also twice Adam’s age then, or 2(a+4).</p>
<p>So, </p>
<p>3a + 4 = 2(a + 4)
3a + 4 = 2a + 8
a = 4</p>
<p>In 1980, Adam was 4, so in 1994, he was 18.</p>
<p>This answer checks out. In 1980, Adam was 4 and Judy was 12. Four years later, he would have been 8, and she would have been 16.</p>
<p>Lets set the problem up like this; where J=Judy and A=Adam.</p>
<p>1980: J=3A
1984: J=2A
1994: A=?</p>
<p>As you can see, 4 years elapse, so lets rewrite these (we will consider 1980 to be t=0, or our initial time reference).</p>
<p>J=3A, (J+4)=2(A+4)
substitution
3A+4=2A+8
A=4</p>
<p>Thus adam was initially (in the year 1980) 4 years old. That means 14 years later (1994) he was 4+14=[18].</p>
<p>I understand everything except the 3a+4 part at the beginning of the equation. If Judy was 3 times as old a sadam (3a), where does +4 come from? There’s already a +4 in the second part to represent 1980 to 1984. I’m very confused.</p>
<p>In 1980, Judy’s age was 3a. In 1984, she was four years older, or 3a+4.</p>
<p>The other a+4 you’re talking about, I assume, is in the 2(a+4); that’s twice as much as Adam’s 1984 age. The a+4 in that expression comes from adding 4 to Adam’s age in 1980; the 2 is from doubling that to find Judy’s age.</p>
<p>The 3a+4 comes from taking Judy’s age in 1980, and adding four to that.</p>
<p>OOOHHH Thanks i get it now. Thanks you guys! :)</p>