the numerator of a fraction is 3 less than the denominator. if 4 us added to the numerator and to the denominator, the resulting fraction is equivalent to 3/4. find the original fraction. Show your solution
the numerator of a fraction is 3 less than the denominator. if 4 us added to the numerator and to the denominator, the resulting fraction is equivalent to 3/4. find the original fraction. Show your solution
Thanks
original fraction ----- (x-3)/x
new fraction = (x-3 + 4)/(x+4) = (x+1)/(x+4)
then (x+1)/(x+4) = 3/4
4x + 4 = 3x + 12
x = 8
the original fraction was .....
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To solve this problem, let's go step by step:
Step 1: Let's assign variables to the numerator and denominator of the fraction. We will assume the numerator is represented by 'x' and the denominator by 'y'.
Step 2: We are given that "the numerator of a fraction is 3 less than the denominator." This can be represented as:
x = y - 3
Step 3: We are also given that "if 4 is added to the numerator and to the denominator, the resulting fraction is equivalent to 3/4." Mathematically, this can be written as:
(x + 4)/(y + 4) = 3/4
Step 4: Now we have two equations:
x = y - 3 (Equation 1)
(x + 4)/(y + 4) = 3/4 (Equation 2)
Step 5: We can substitute Equation 1 into Equation 2:
((y - 3) + 4)/(y + 4) = 3/4
Step 6: Simplifying Equation 5, we get:
(y + 1)/(y + 4) = 3/4
Step 7: Cross-multiply to get rid of fractions:
4(y + 1) = 3(y + 4)
Step 8: Expand and solve for y:
4y + 4 = 3y + 12
4y - 3y = 12 - 4
y = 8
Step 9: Substitute the value of y back into Equation 1 to find x:
x = y - 3
x = 8 - 3
x = 5
Step 10: Therefore, the original fraction is 5/8.
In summary, the original fraction is 5/8.