The sum of the numerator and denominator of a fraction is 17. If 3 is added to the numerator, the value of the fraction will be 1. What is the fraction? Explain your workings.

let the fraction be a/b

we are told a+b=17

and (a+3)/b = 1
a+3 = b

back in a+b=17
a + a+3 = 17
2a = 14
a = 7
then b= 10

Your fraction is 7/10

Well, well, well. Looks like we have a little math problem on our hands. Let's solve it together, shall we?

Let's call the numerator of our fraction "x" and the denominator "y." According to the problem, the sum of the numerator and denominator is 17. So, we can write an equation: x + y = 17.

Now, we're also told that if we add 3 to the numerator, the fraction becomes 1. This means that if we take the new numerator (x + 3) and divide it by the denominator (y), we should get 1. Another equation for you: (x + 3) / y = 1.

Now let's put our math hats on and solve this system of equations. We can start by rearranging the second equation, which gives us x + 3 = y.

Now we can substitute this into the first equation: (x + 3) + x = 17. If we simplify this, we get 2x + 3 = 17.

Subtracting 3 from both sides of the equation, we find that 2x = 14.

Finally, divide both sides of the equation by 2, and we're left with x = 7.

Now, we can substitute this value of x back into our rearranged equation: 7 + 3 = y.

So, y = 10.

Therefore, the fraction is 7/10.

And voila! That's how you juggle numbers and find the fraction using some math magic.

Let's represent the fraction as "x/y", where x is the numerator and y is the denominator.

According to the given information, the sum of the numerator and denominator is 17:
x + y = 17 -- (equation 1)

If 3 is added to the numerator, the value of the fraction becomes 1:
(x + 3) / y = 1

We can simplify this equation by multiplying both sides by y:
x + 3 = y -- (equation 2)

Now we have a system of two equations (equation 1 and equation 2) with two variables (x and y). We can solve this system to find the values of x and y.

From equation 2, we can substitute the value of y in equation 1:
x + (x + 3) = 17
2x + 3 = 17

Next, we can subtract 3 from both sides of this equation:
2x = 14

Then divide both sides by 2:
x = 7

Now we can substitute the value of x in equation 2 to find the value of y:
7 + 3 = y
y = 10

Therefore, the fraction is 7/10.

To find the fraction, we need to set up equations based on the given information and solve them simultaneously.

Let's assume the fraction is represented as "x/y", where x is the numerator and y is the denominator.

According to the problem, the sum of the numerator and denominator is 17. So, we have the equation: x + y = 17. (Equation 1)

Next, it is stated that if 3 is added to the numerator, the value of the fraction will be 1.

When 3 is added to the numerator, the fraction becomes (x + 3)/y. According to the problem, this fraction is equal to 1, which can be expressed as 1/1. So, we have the equation: (x + 3)/y = 1. (Equation 2)

Now, we have a system of two equations (Equation 1 and Equation 2) with two variables (x and y). We can solve this system by substituting one equation into the other or by using the substitution or elimination method.

Let's use the substitution method to solve these equations:

From Equation 1, we can express x in terms of y: x = 17 - y.

Substituting this value of x in Equation 2, we get: (17 - y + 3)/y = 1.

Simplifying this equation, we have: (20 - y)/y = 1.

Cross-multiplying, we get: 20 - y = y.

Bringing all the y terms to one side, we have: 20 = 2y.

Dividing both sides by 2, we get: y = 10.

Substituting this value of y back into Equation 1, we find: x + 10 = 17.

Subtracting 10 from both sides, we get: x = 7.

Therefore, the fraction is 7/10.

So, the fraction is 7/10.

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