<p>I'm not entirely sure if this is the correct place to post this, so if not, I'm really sorry.</p>
<p>Ok, so I there are two problems I need help with. Both problems come from the new Blue Book (the one that came out July 2009). I just can't seem to solve numbers 13 (pg 641) and 17 (pg 642) in section 2 of practice test number 5.</p>
<p>Here are the problems:</p>
<ol>
<li>The total daily cost c, in dollars, of producing x units of a certain product is given by the function c(x) 5 ((600x-200)/x) 1 k, where k is a constant and x does not equal 100. If 20 units were produced yesterday for a total cost of $640, what is the value of k?</li>
</ol>
<p>(A) 40
(B) 50
(C) 60
(D) 590
(E) 640</p>
<p>The answer is supposed to be (B), but I just can't solve it.</p>
<ol>
<li>In the xy-plane, line L passes through the origin and is perpendicular to the line
4x + y = k, where k is a constant. If the two lines intersect at the point (t, t + 1), what is the value of t?</li>
</ol>
<p>(A) -4/3
(B) -5/4
(C) 3/4
(D) 5/4
(E) 4/3</p>
<p>The answer is supposed to be (E), but I don't know how to go about solving it.</p>
<p>Again, sorry if this is not allowed. However, any and all help would be greatly appreciated.</p>
<p>I dont feel like looking up the first problem (I am not quite clear on what that function means since you dont have an equal sign and its all discombobulated )
As to #2, recall the property of the slope of a line perpendicular to the given line. It will be the reciprocal of the original slope with inverted sign. Thus, the slope of original line (-4) turns into 1/4. Since it passes through the origin, its k will be zero. Thus the equation of the second (perpendicular) line is y=(1/4)x. Plug the (t+1) for y and t for x and solve the equation for t to get 4/3 as the answer.</p>
<p>YAHA is right that the second line is y = (1/4)x. However, plugging in (t,t+1) gives t+1 = (1/4)t, and solving gives (3/4)t = -1 or t = -4/3. If the point of intersection were (t,t-1) the answer would be (E).</p>
<p>Thank you so much for the prompt replies. I was also confused with number 13 myself since it did not have an equal in the actual practice test either. I don’t know if that is intentional or a misprint on The College Board’s part though.</p>
<p>I think the function should read c(x)=5 ((600x-200)/x) 1 k, but I’m still not 100% positive.</p>
<p>But thanks for helping with number 17, I really appreciate it. Also, I realized the answer is (A) after a second look at the answer key (guess that wasn’t so smart on my part).</p>
<p>Actually, this question would be interesting if TCB asked us to correct the equation and find the answer. It would, however, go beyond what is tested on the SAT. </p>
<p>Fwiw, the question should have read, if the TCB editors had not been careless when converting the digital images into text. </p>
<p>The total daily cost c, in dollars, of producing x units of a certain product is given by the function c(x) = ((600x-200)/x) + k, where k is a constant and x is not 100. If 20 units were produced yesterday for a total cost of $640, what is the value of k ?</p>
<p>The problem is easily solved by placing the known values in the formula.</p>
<p>640 = ((600*20)-200)/20) + k
640 = 590 + k
640 - 590 = k</p>
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