A mother is 21 years older than her new born daughter. How old will the daughter be when her age is 1/4 of her mother's?
Let x = daughter's age and x + 21 = mother's age.
x = 1/4(x + 21)
Solve for x.
Show
Let's break down the information provided and solve the problem step by step.
We are given that the mother is 21 years older than her newborn daughter. So, we can express the relationship between their ages as:
Mother's age = Daughter's age + 21
Next, we need to find the age at which the daughter's age becomes one-fourth of her mother's age. Let's call this age "x".
We can express this situation using the equation:
Daughter's age + x = (1/4)(Mother's age + x)
Substituting the relationship between their ages, we get:
Daughter's age + x = (1/4)(Daughter's age + 21 + x)
Multiplying both sides of the equation by 4 to get rid of the fraction, we have:
4(Daughter's age + x) = Daughter's age + 21 + x
Expanding the brackets, we get:
4Daughter's age + 4x = Daughter's age + 21 + x
Rearranging the terms, we have:
3Daughter's age = 21 - 3x
Next, we need to find the value of x so that the daughter's age becomes one-fourth of the mother's age. To do this, we set the expression for the daughter's age (3Daughter's age) equal to one-fourth of the daughter's age + 21 (1/4)(Daughter's age + 21):
3Daughter's age = (1/4)(Daughter's age + 21)
Multiplying both sides of the equation by 4 to eliminate the fraction, we get:
12Daughter's age = Daughter's age + 21
Rearranging the terms, we have:
11Daughter's age = 21
Dividing both sides of the equation by 11, we find that the daughter's age is:
Daughter's age = 21 / 11 = 1.91 (rounded to two decimal places)
Since the daughter's age cannot be in decimal form, we round it down to the nearest whole number. Thus, the daughter's age is 1 year.
Finally, we can substitute the daughter's age (1 year) into the equation we derived earlier to find the value of x:
3Daughter's age = 21 - 3x
3 * 1 = 21 - 3x
3 = 21 - 3x
3x = 21 - 3
3x = 18
x = 18 / 3
x = 6
Therefore, when the daughter is 6 years old, her age will be one-fourth of her mother's age.
To solve this problem, we need to break it down into steps:
Step 1: Represent the current ages of the mother and daughter
Let's assume the daughter's current age is x years. According to the problem, the mother is 21 years older than her newborn daughter, so the mother's current age is x + 21 years.
Step 2: Find the equation representing the daughter's age when it's 1/4 of her mother's age
To find the daughter's age when it is 1/4 of her mother's age, we multiply the mother's age by 1/4. Therefore, the equation representing the daughter's age is: x = (1/4) * (x + 21)
Step 3: Solve the equation
To solve the equation, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 4: 4 * x = x + 21.
Expanding the equation gives us: 4x = x + 21
Next, we will isolate x by subtracting x from both sides of the equation: 4x - x = 21
Simplifying the equation gives us: 3x = 21
Finally, divide both sides of the equation by 3 to solve for x: x = 21 / 3
Therefore, the daughter's current age is 7 years old.
Step 4: Calculate the daughter's age when it's 1/4 of her mother's age
Now that we know the daughter's current age is 7, we can substitute this value into the equation we obtained earlier to find her age when it's 1/4 of her mother's age: x = (1/4) * (x + 21)
Substituting x = 7, we get: 7 = (1/4) * (7 + 21)
Simplifying the equation gives us: 7 = (1/4) * 28
Now, multiply both sides of the equation by 4 to get rid of the fraction: 4 * 7 = 28
Simplifying further: 28 = 28
Therefore, the daughter will be 7 years old when her age is 1/4 of her mother's age.