sum of ages of mother and daughter is 32 years.Daughter is a year old.In how many years will mother be 4 times daughters age(use one variable only)
31+x = 4(1+x)
x=4
31+x=4(1+x)
32=(4)(2)
32=8
32/8 = 8/8
x=4
Let's assign a variable to represent the daughter's age. Let's call it "x."
According to the given information, the sum of the mother and daughter's ages is 32 years. Since the daughter is a year old, we can write the equation as:
x + (1 + x) = 32
Simplifying this equation, we get:
2x + 1 = 32
Now, let's solve for x:
2x = 32 - 1
2x = 31
Dividing by 2 on both sides:
x = 31 / 2
x = 15.5
Therefore, the daughter's age is 15.5 years.
To find out how many years it will take for the mother to be four times her daughter's age, we can use the variable "y" to represent the number of years.
After y years, the daughter's age will be (15.5 + y) and the mother's age will be (15.5 + y) + y.
According to the problem, the mother will be four times the daughter's age, so we can set up the equation:
(15.5 + y) + y = 4(15.5 + y)
Simplifying this equation, we get:
15.5 + 2y = 62 + 4y
Rearranging the terms:
4y - 2y = 62 - 15.5
2y = 46.5
Dividing by 2 on both sides:
y = 46.5 / 2
y = 23.25
Therefore, it will take approximately 23.25 years for the mother to be four times her daughter's age.