<p>These are taken from some 1993 practice tests.</p>
<li><p>Pat and Lee are removing cartons from a truck. If Pat removes 1/8 of the number of cartons from the truck and Lee removes 1/4 of the number of cartons, there are 40 cartons left. How many cartons were originally in the truck?
Answer: 64</p></li>
<li><p>(a^6)=5 and (a^5)=4/x which of the following is an expression for “a” in terms of “x”
answer: 5x/4</p></li>
<li><p>If the average (arthmetic mean) of a,b,c=10 and the average of a,b,2c=14 what is the average of a and b?
answer: 9</p></li>
</ol>
<p>All three questions are rated “hard” by college board.</p>
<ol>
<li><p>If x is the original #cartons, removal of x/8 + x/4 or 3x/8 cartons leaves behind 5x/8, which = 40
So x = (8)(40)/5 = 64 . </p></li>
<li><p>a^6 = (a^5)(a) = 5, so a^5 = 5/a. Plug this into the 2nd equation to get 5/a = 4/x or 5x = 4a or a = 5x/4 .</p></li>
<li><p>(a+b+c)/3 = 10, so a+b+c = 30
(a+b+2c)/3 = 14, so a+b+2c = 42
Subtract Eqn(1) from Eqn(2) to get c = 42-30 = 12.
Plug in c=12 into Eqn(1) to get a+b+ 12=30, or a+b = 18
so (a+b)/2 = 9</p></li>
</ol>
<p>for number 2:
well, because of the laws of exponents, (a^6)/(a^5)= a. so by substitution, a will equal (5)/(4/X) which equals 5/4X. I just thought I would explain it a different way to see if that helps.</p>
<p>Let's multiply all the numbers by 8:
8 trucks to start with,
Pat removes (1/8)<em>8=1 truckful,
Lee removes (1/4)</em>8=2 truckfuls,
8-1-2=5 unloaded trucks are left with 40*8=320 cartons total.
320/5 = 64 cartons in one truck.</p>