the numerator of a fraction is 3 less than the denominator. when 7 is added to the numerator and the denominator, the fraction becomes 6/7. find the original fraction.

11/14

Step-by-step explanation:

Let's say our fraction is x/y

numerator (x) is 3 less than (-3 +) the denominator (y)

x = -3 + y

x = y - 3

when 7 is added (+7) to the numerator and denominator (x and y), the fraction becomes 6/7 (=6/7)

add 7 to the numerator and denominator of the original fraction, set that equal to 6/7

(x+7)/(y+7) = 6/7

x = y - 3

plug y-3 in for x into the first equation

(y-3+7)/(y+7)=6/7

(y+4)/(y+7)=6/7

multiply both sides by 7 to remove a denominator

(7y+28)/(y+7) = 6

multiply both sides by (y+7) to remove the other denominator

7y+28 = 6y + 42

subtract 6y from both sides to put all variable values on one side

y + 28 = 42

subtract 28 from both sides to isolate y

y = 14

x = y - 3

x = 11

original fraction = 11/14

11/14

Step-by-step explanation:

Set up an equation: (y-3)+7 / y +7 = 6/7*Since the numerator is  3 less than y and both sides is added by 7 to get 6/7*

Simplify the best as you can: y+4 / y+7 = 6/7 *You can see that 4 is 3 less than 7 right now*

Cross multiply: 7(y+4) = 6(y+7)

Distribute: 7y+28 = 6y+42

Solve for y: 7y-6y = 42-28

                          y = 14

If y is 14, then the numerator is 11 because 14-3 is 11

11/14 is your answer

Check:

11+7 / 14+7 is 18/21 which simplifies to 6/7 when you divide by 3

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step-by-step explanation: