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The numerator of a positive fraction is 3 less than its denominator. When both the numerator and denominator are increased by 4, the fraction is increased by 4/15. Find the original fraction.

a) 5/8
b) 7/10
c) 9/12
d) 11/14

User Sublime
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1 Answer

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Final answer:

To solve the problem, assume the original fraction is x/y. Use the given information to set up an equation and solve for y. Substitute the value of y back into the equation x = y - 3 to find x. The original fraction is x/y.

Step-by-step explanation:

To solve this problem, let's assume the original fraction is x/y, where x is the numerator and y is the denominator.

According to the given information, x = y - 3.

When both the numerator and denominator are increased by 4, the new fraction is (x + 4) / (y + 4). We also know that this new fraction is increased by 4/15.

Setting up the equation, we have: (x + 4) / (y + 4) = x/y + 4/15.

Substituting the value of x from the first equation, we have: (y - 3 + 4) / (y + 4) = (y - 3)/y + 4/15.

Simplifying this equation, we get: (y + 1) / (y + 4) = (15y - 45 + 4y) / (15y).

By cross-multiplication, we can solve for y.

After finding the value of y, substitute it back into the equation x = y - 3 to get the value of x.

The original fraction is x/y.

User Loli
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