When we look at this thing for the first time, it looks like it's going to be a dog of a bear to solve, because 'q' is buried inside a squared term and a cubed term.
But this is why it's so important to learn that in math, you DON't immediately ignite your hair and go running around in circles as soon as you see the problem. The first thing you have to do <u>every</u> time is sit still, look at the problem, breathe air, and switch your brain into the 'ON' position.
Look at that big ugly fraction in the equation. Can it be simplified ? You betcha it can ! The quantity (q+r) is a factor of the numerator and denominator, so we can do some canceling.
Divide the top and the bottom of the fraction by (q+r)², and then the problem says . . .
<em>p = (q+r)/12 + 4r</em>
which is MUCH easier to unravel and solve for 'q' . Let's do this !
p = (q+r)/12 + 4r
Subtract (q+r)/12 from each side . . . p - (q+r)/12 = 4r
Subtract 'p' from each side . . . -(q+r)/12 = 4r - p
Multiply each side by -1 . . . (q+r)/12 = p - 4r
Multiply each side by 12 . . . (q+r) = 12p - 48r
Subtract 'r' from each side . . . <em>q = 12p - 49r</em>
<h3>
Answer: Choice B) 1/8 and 1/4 are not equivalent</h3>
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Explanation:
There are two ways to check to see if two fractions are equal.
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Method 1) Cross multiplication
3/6 = 2/4
3*4 = 6*2
12 = 12
The last equation is true, so the first equation is true. This shows 3/6 and 2/4 are the same fraction
1/8 = 1/4
1*4 = 8*1
4 = 8
The last equation is false, so 1/8 = 1/4 is false. We found our answer.
1/3 = 2/6
1*6 = 3*2
6 = 6
This equation is true. So we can move on
1/4 = 3/12
1*12 = 4*3
12 = 12
A similar story happens with A and C.
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Method 2) Comparing decimal forms
Using a calculator, we can find the decimal form of any fraction
3/6 = 0.5 and 2/4 = 0.5; since we get the same decimal value both times, this means 3/6 = 2/4 is a true statement. Choice A is ruled out.
1/8 = 0.125 and 1/4 = 0.25; we get different decimal values, so we can see that choice B is the answer
1/3 = 0.333.... (the 3s go on forever) and 2/6 = 0.333... we have the same story as choice A, so we can rule out choice C.
1/4 = 0.25 and 3/12 = 0.25, same story as A and C. We can rule out choice D.
Answer:
640 = 0.80·j
Step-by-step explanation:
Let j represent the cost of Jocelyn's computer (in dollars). Adriana's computer cost 20% less, so has a cost that is 0.80·j. We are told that amount is $640, so we can write the equation ...
640 = 0.80·j
The answer is the first choice
