Thendmonimator of a fraction is 1 more than the numerator. If the numerator is decreased by 1, the value of the resulting fraction is 3/4. What is the original fraction?
P4,000 is borrowed for 75 days at
16% per annum simple interest.
How much will be due at the end of
75 days?
Let's solve this step by step:
Let's assume the original fraction is x/y, where x is the numerator and y is the denominator.
According to the given information, the denominator is 1 more than the numerator. So, we can write the equation as:
y = x + 1 ...(Equation 1)
Now, it is given that when the numerator is decreased by 1, the resulting fraction is 3/4. So, we can set up another equation:
(x - 1) / y = 3/4
We can substitute the value of y from Equation 1 into this equation:
(x - 1) / (x + 1) = 3/4
Now, we can cross-multiply:
4(x - 1) = 3(x + 1)
Expanding both sides of the equation:
4x - 4 = 3x + 3
Moving all the terms to one side:
4x - 3x = 3 + 4
x = 7
Now, substitute the value of x back into Equation 1 to find the value of y:
y = x + 1 = 7 + 1 = 8
Therefore, the original fraction is 7/8.
To solve this problem, let's start by assigning variables to the numerator and denominator of the fraction.
Let x be the numerator and y be the denominator.
We know that the denominator is 1 more than the numerator, so we can write the equation:
y = x + 1 ... (Equation 1)
Next, we are told that if the numerator is decreased by 1, the resulting fraction is 3/4. This can be represented by the equation:
(x - 1) / y = 3/4 ... (Equation 2)
We can solve this system of equations using substitution.
First, substitute the value of y from Equation 1 into Equation 2:
(x - 1) / (x + 1) = 3/4
Now, cross-multiply to get rid of the fractions:
4(x - 1) = 3(x + 1)
Expand both sides:
4x - 4 = 3x + 3
Combine like terms:
4x - 3x = 3 + 4
x = 7
Now, substitute the value of x back into Equation 1 to find y:
y = 7 + 1
y = 8
So, the original fraction is 7/8.
numerator ----- x
denominator ---- x+1
fraction = x/(x+1)
if (x-1)/(x+1) = 3/4
4x - 4 = 3x + 3
x = 7
original fraction = 7/8
check: 6/8 = 3/4, my answer is correct