The numerator of a fraction is 4 less than its denominator. If both the numerator and
the denominator of the fraction are increased by 2, then the resulting fraction is equal
to 3/5. What is the fraction? Write an equation that will represent the problem.
(d-4+2)/(d+2) = 3/5
d=8, so the fraction is 4/8
check: 6/10 = 3/5
2. Paulo drove 75 km from Tanauan, Batangas to Lucban, Quezon to visit his cousins.
His average speed for the trip to Lucban was 10 km/h faster than on his way back to
Tanauan, and as a result, his return trip took 2 hours longer. What is his average
speed for the trip to Lucban? Write the equation that will represent the function.
Well, isn't this just a fraction frenzy! Let's break it down.
Let's call the numerator of our mysterious fraction "x" and the denominator "y". According to the problem, the numerator is 4 less than the denominator, so we can write an equation:
x = y - 4
Now, it says that if we increase both the numerator and the denominator by 2, we get the fraction 3/5. So our new equation becomes:
(x + 2) / (y + 2) = 3/5
And there you have it! Our equation has arrived. Now, let's solve this mathematical mystery and find the fraction.
To solve this problem, let's start by writing an equation to represent the given information:
Let's assume the denominator of the fraction is represented by 'x'.
Since the numerator is 4 less than the denominator, it can be represented by 'x - 4'.
So, the original fraction can be represented as (x - 4)/x.
According to the problem, when both the numerator and the denominator are increased by 2, the resulting fraction is equal to 3/5. So, the new fraction can be represented as (x - 4 + 2)/(x + 2).
Now we can write the equation to represent the problem:
(x - 4 + 2)/(x + 2) = 3/5
To find the value of 'x' and ultimately the fraction, we can solve this equation.
1. The numerator of a fraction is 4 less than its denominator. If both the numerator and
the denominator of the fraction are increased by 2, then the resulting fraction is equal
to 3/5. What is the fraction? Write an equation that will represent the problem.
2. Paulo drove 75 km from Tanauan, Batangas to Lucban, Quezon to visit his cousins.
His average speed for the trip to Lucban was 10 km/h faster than on his way back to
Tanauan, and as a result, his return trip took 2 hours longer. What is his average
speed for the trip to Lucban? Write the equation that will represent the function.