World Problem Math Algebra Fraction The denominator of a fraction in simplest form is greater than

dokezwa17

dokezwa17

Answered question

2022-05-29

World Problem Math Algebra Fraction
The denominator of a fraction in simplest form is greater than the numerator by 3. If 7 is added to the numerator, and 5 added to the denominator, then the fraction itself is increased by 1 2 . Find the original fraction.
I got the equation x x + 3 = 2 x + 14 x + 8
When I solve this, I get a weird answer. My equation might be wrong. Can someone help me?

Answer & Explanation

Haleigh Vega

Haleigh Vega

Beginner2022-05-30Added 13 answers

Suppose the fraction (in simplest form) is a b
Then from the first statement
b = a + 3
From the second statement
a + 7 b + 5 = 1 2 + a b
You know have a simple system of equations which you can solve.
Kash Brennan

Kash Brennan

Beginner2022-05-31Added 4 answers

Let x be the numerator. Then:
x x + 3 + 1 2 = x + 7 x + 8
1 2 ( x + 8 ) ( x + 3 ) + x ( x + 8 ) = ( x + 3 ) ( x + 7 )
Then solve the quadratic equation.

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