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Nostrana [21]
2 years ago
11

The numerator of a certain fraction is to its denominator as 2 to 3; if 5 be added to the numerator the ratio will be as 3 to 2;

what is the fraction?
Mathematics
1 answer:
vova2212 [387]2 years ago
6 0
N= numerator
D= denominator

N:D ==> 2:3

2:3, 4:6, 6:9... And so on...

The pattern here is that the numerator increases by 2 and the denominator by 3. Easy right?

Now 5 is added to the "n".

Now it is N:D ==> 3:2

3:2, 6:4, 9:6... And so on...

The pattern here is inverted then the 2:3 one.

If I'm right then which one (you might have to continue the process/pattern) then one of them will increase by 5.

3 => 2 = +1 (2+1=3)
6 => 4 = +2 (4+2=6)
9 => 6 = +3 (6+3=9)
12 => 8 = +4 (8+4=12)
15 => 10 = +5 (10+5=15)
18 => 12= +6 (12+6=18)

Q. Which one is +5?

A. 15:10

That is what "I" think it is.

Now, the question is,
Does it work? Does it fit the above description?

Q. Does it even work? Does it fit the above description?
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Ken normally leaves work at 5:00 pm, but he is leaving 20 minutes late today. He decides to make up time by taking the toll road
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Answer:

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Step-by-step explanation:

As stated in the question that x represents the number of minutes his <em>normal</em> commute takes. Here the keyword is normal; in the <em>normal</em> commute, Ken takes side streets instead of the toll road.

However, in this scenario, we have to come up with the equation that takes Ken's commute via <em>toll road</em>.

Ken can travel 3 times faster by taking the toll road (Given), which can be represented in the mathematical terms in terms of x as follows:

x_{toll\_road}=\frac{1}{3}x

<em>Without considering Ken getting late, </em>the equation would become the following:

y=\frac{1}{3} x --- (A)

<em>As Ken is leaving late</em>, we have to incorporate that time as well by <em>adding</em> it in the aforementioned equation (A).

In this case, it's 20 minutes; therefore, the equation (A) will become:

y=\frac{1}{3} x+20

Hence, the correct answer is y=\frac{1}{3} x + 20.

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