(Show all workings) 1/4 of morolake’s age nine years ago is the same as 1/5 of her age next year. What is morolake age now
Let Morolake's age now be x
1/4 of Morolake's age nine years ago = (x-9)/4
1/5 of her age next year = (x+1)/5
Equating the two:
(x-9)/4 = (x+1)/5
5(x-9) = 4(x+1)
5x - 45 = 4x + 4
x = 49
Morolake's age now is 49.
Let's assume Morolake's current age is represented by "x".
Step 1: Determine Morolake's age nine years ago
Morolake's age nine years ago can be represented as "x - 9".
Step 2: Determine 1/4 of Morolake's age nine years ago
1/4 of Morolake's age nine years ago is (1/4) * (x - 9).
Step 3: Determine Morolake's age next year
Morolake's age next year can be represented as "x + 1".
Step 4: Determine 1/5 of Morolake's age next year
1/5 of Morolake's age next year is (1/5) * (x + 1).
Step 5: Set up the equation based on the given information
According to the problem statement, 1/4 of Morolake's age nine years ago is the same as 1/5 of her age next year. Therefore, we can write the equation:
(1/4) * (x - 9) = (1/5) * (x + 1).
Step 6: Solve the equation
To solve this equation, we can start by eliminating the fractions. We can do this by multiplying both sides of the equation by the denominators in order to cancel out the fractions:
5 * (1/4) * (x - 9) = 4 * (1/5) * (x + 1).
Simplifying both sides:
(5/4) * (x - 9) = (4/5) * (x + 1).
Expanding both sides:
(5/4) * x - (5/4) * 9 = (4/5) * x + (4/5) * 1.
Multiplying:
(5/4) * x - (45/4) = (4/5) * x + (4/5).
Step 7: Continue solving the equation
To isolate the variable, we can first get rid of the fractions by multiplying both sides of the equation by the least common denominator (LCD) of 4 and 5, which is 20:
20 * ((5/4) * x - (45/4)) = 20 * ((4/5) * x + (4/5)).
Simplifying both sides:
20 * (5/4) * x - 20 * (45/4) = 20 * (4/5) * x + 20 * (4/5).
Multiplying:
25x - 225 = 16x + 16.
Step 8: Further solve the equation
To solve for "x," we can start by rearranging the equation and combining like terms:
25x - 16x = 225 + 16.
9x = 241.
Dividing both sides by 9:
x = 241/9.
Step 9: Determine Morolake's current age
Finally, we can simplify the fraction to determine Morolake's current age:
x = 26 remainder 5.
Therefore, Morolake's age now is 26 years old.
Let Morolake's current age be represented by "x".
According to the given information, 1/4 of Morolake's age nine years ago is the same as 1/5 of her age next year.
Let's break it down:
Nine years ago, Morolake's age was x - 9.
1/4 of Morolake's age nine years ago is (1/4)*(x - 9).
Next year, Morolake's age will be x + 1.
1/5 of Morolake's age next year is (1/5)*(x + 1).
According to the problem, (1/4)*(x - 9) is equal to (1/5)*(x + 1).
We can solve this equation to find the value of x.
Multiply both sides of the equation by 20 to eliminate the denominators:
20 * (1/4)*(x - 9) = 20 * (1/5)*(x + 1)
5(x - 9) = 4(x + 1)
Now, distribute and simplify:
5x - 45 = 4x + 4
Subtract 4x from both sides:
5x - 4x - 45 = 4 - 4x + 4x
x - 45 = 4
Add 45 to both sides:
x - 45 + 45 = 4 + 45
x = 49
Morolake's current age is 49.