<li>Meghan’s car mechanic charges “a” dollars for a consultation, which always lasts “b” hours, and then charges “c” dollars per hour for any additional time needed to work on the car. If Meghan’s car cost $900 to fix, whih of the following expressions represents the number of hours and mechanic spent working on her car?</li>
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<li><p>(B) 2a+14
If we let x = Sylvia's age 8 years ago, x=2(a+3). I'm not sure how detailed you want this, so (a+3) is Adam's age three years in the future. This gives us x=2a+6; however this is S's age 8 years ago so we need to add 8. This leaves us with 2a+14</p></li>
<li><p>D I'm assuming that 'working on the car' includes consultation.
900=a+c<em>hours
Solving for h, we get h=(900-a)/c; This is answer A and would be right if the consultation doesn't count. But I think it does, so we add b - the length of the consultation.
Total Time = ((900-a)/c)+b
This is the same as D, but they just created a like denominator - (b</em>c)/c=b.</p></li>
<li><p>A - I only
P is negative and q is positive - I typically pick numbers for these questions and just try things out. 2 multiplied by any negative will always be less than two multiplied by a positive. II is not always true (-4)^2=16, which is greater than 2^2=4. For three, the numbers would have to be = and opposite - ex)-3 and 3</p></li>
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<p>If I am wrong, I would appreciate it if any following posters would explain where I made the mistakes.</p>
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<li><p>I agree with the previous poster on choice (B). I prefer substitution than variable, so here's how I got it: lets say Sylvia was 20 years old eight years ago, she is 28 years old now. Divide 20 by 10 and subtract 3 from that to get Adam's age now, which is 7. Substitute 7 into choice (B) and you get 28, Sylvia's age.</p></li>
<li><p>I got (A) for this one. Again, substitution. I substituted 200 for a, 4 for b, and 70 for c (totally random guess, but I was lucky to get a integer as my "target number"). So take the total, $900 subtract the initial $200. That is four hours. Take your answer from step 1 ($700) and divide it by c, which is 70, and get 10. 4+10 = 14. If you substitute a, c into choice (A), you get 14.</p></li>
<li><p>again, I agree with the previous poster that choice (A) is correct. I picked -1 for p and 5 for q to substitue, eliminating choice III. Then, I substituted -1 for p and 1 for q, eliminating choice II. Just to make sure, I did a little bit of reasoning here: p must be negative, q must be positive. 2p<2q can be simplified to p<q, which is true.</p></li>
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