The sum of the age of a woman and her daughter is 46 years.In 4 years the ratio of their age will be 7:2.How many years time will the sum of their age be 66 years
well to make it easy just add 10 to each so in ten years:
but if you insist
w + d = 46
(w+4)/(d+4) = 7/2
d = (46 - w)
(w+4) / (50-w) = 7/2
2 w + 8 = 350 - 7 w
9 w = 342
w = 38
d = 46 - 38 = 8
now
8+x + 38 + x = 66
46 +2x = 66
2x = 20
x = 10
remarkable :)
*GASPS* 🙀
To solve this problem, let's break it down step by step:
Step 1: Understand the problem and the given information.
We are given two pieces of information:
- The sum of the woman's and her daughter's current ages is 46 years.
- In 4 years, the ratio of their ages will be 7:2.
Step 2: Find the current ages of the woman and her daughter.
Let's assume the current age of the woman is W years and the current age of her daughter is D years.
Given that the sum of their ages is 46, we can set up a simple equation:
W + D = 46
Step 3: Calculate the ages in 4 years.
In 4 years, the woman's age will be W + 4 and the daughter's age will be D + 4.
Step 4: Set up a ratio equation based on the information given after 4 years.
The ratio of their ages in 4 years is given as 7:2. So we can set up the following equation:
(W + 4) / (D + 4) = 7 / 2
Step 5: Solve the equations.
First, solve the equation W + D = 46 for one variable.
W = 46 - D
Now substitute this value of W in the ratio equation:
(46 - D + 4) / (D + 4) = 7 / 2
Now cross-multiply:
2(46 - D + 4) = 7(D + 4)
Simplify and solve for D:
92 - 2D + 8 = 7D + 28
-2D - 7D = 28 - 92 - 8
-9D = -72
D = -72 / -9
D = 8
Substitute the value of D back into W + D = 46 to find W:
W + 8 = 46
W = 46 - 8
W = 38
Therefore, the current ages of the woman and her daughter are 38 years and 8 years, respectively.
Step 6: Find how many years it will take for the sum of their ages to be 66.
Let's assume that after x years, the sum of their ages will be 66.
Their ages will become (W + x) and (D + x).
Set up the equation based on the assumption:
(W + x) + (D + x) = 66
Substitute the values of W and D:
(38 + x) + (8 + x) = 66
Combine like terms:
38 + 8 + 2x = 66
Simplify and solve for x:
46 + 2x = 66
2x = 66 - 46
2x = 20
x = 20 / 2
x = 10
Therefore, it will take 10 years for the sum of their ages to become 66 years.