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

stew reads at the fastest rate of 265 words per minute.

step-by-step explanation:

it's a given that felicia reads at 260 word per minute and on connie's graph we can see that she reads 200 words per minute. since stew's table tells us that he read 795 in 3 minutes, we can divide 795 by 3 to find out how many words he reads per minute.

795/3 = 265

stew reads 265 words per minute - he reads at the fastest rate since felecia reads at 260 words per minute and connie reads at 200 words per minute.

stew (265) > felecia (260) > connie (200)