# A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to th

Discussion in 'Calculator Requests' started by math_celebrity, Jan 3, 2022.

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A fraction has a value of 3/4. If 7 is added to the numerator, the resulting fraction is equal to the reciprocal of the original fraction. Find the original fraction.
Let the fraction be x/y. We're given two equations:
1. x/y = 3/4
2. (x + 7)/y = 4/3. (The reciprocal of 3/4 is found by 1/(3/4)
Cross multiply equation 1 and equation 2:
1. 4x = 3y
2. 3(x + 7) = 4y
Simplifying, we get:
1. 4x = 3y
2. 3x + 21 = 4y
If we divide equation 1 by 4, we get:
1. x = 3y/4
2. 3x + 21 = 4y
Substitute equation (1) into equation (2) for x:
3(3y/4) + 21 = 4y
9y/4 + 21 = 4y

Multiply the equation by 4 on both sides to eliminate the denominator:
9y + 84 = 16y

To solve this equation for y, we type it in our math engine and we get:
y = 12

We then substitute y = 12 into equation 1 above:
x = 3 * 12/4
x = 36/4
x = 9

So our original fraction x/y = 9/12