"the sum of the age of a mother and a daughter is 44 years. three years ago the product of their ages was 192.how old is the daughter now? plsssss show working"
m + d = 44 ... m = 44 - d
(m - 3)(d - 3) = 192 ... substituting ...(41 - d)(d - 3) = 192
... 41 d - d^2 -123 + 3 d = 192 ... d^2 - 44 d + 315 = 0
use the quadratic formula to find the ages
The total age of Cheko and Miko is 44 years.
Three years ago, Cheko was older
than Miko by 20 years.
How old are they now?
Cheko have some 10-cent and 20-cent coins.
The coins add up to $2.10.
There are three more 10-cent than 20-cent coins.
How many 10-cent coins and 20-cent coins does Cheko have?
Mr. Noel always saves 6/11
of his monthly salary. If his monthly salary is increased by $298, his monthly savings will be $4572. How much is Mr Noel's monthly salary before the increase?
1 plus 1 in binary number
1+1 in binary
Sum of ages of father, mother and daughter = 100. Five years interval between them each. How many years is the daughter?
To find the age of the daughter, let's name the mother's age as "M" and the daughter's age as "D". We are given that the sum of their ages is 44 years, so we can write this as:
M + D = 44
We are also given that three years ago, the product of their ages was 192. So, three years ago, the mother's age would be (M - 3) and the daughter's age would be (D - 3). The product of their ages can then be written as:
(M - 3)(D - 3) = 192
Now, we have two equations:
M + D = 44 (Eq. 1)
(M - 3)(D - 3) = 192 (Eq. 2)
To find the age of the daughter, we will solve this system of equations using the substitution or elimination method.
Let's solve by the elimination method. We will multiply Eq. 1 by -1 and add it to Eq. 2 to eliminate the "M" variable:
-1(M + D) + (M - 3)(D - 3) = -44 + 192
Simplifying this equation gives us:
- (M + D) + (MD - 3M - 3D + 9) = 148
Now, let's simplify further:
MD - 3M - 3D - M - D + 9 = 148
Rearranging the terms, we get:
MD - 4M - 4D = 139 (Eq. 3)
Next, we can substitute Eq. 1 into Eq. 3 to eliminate the "M" variable:
D(44 - D) - 4(44 - D) - 4D = 139
Expanding this equation gives us:
44D - D^2 - 176 + 4D - 4D = 139
Simplifying further:
D^2 - 44D - 139 + 176 = 0
Rearranging and combining the terms, we have a quadratic equation:
D^2 - 44D + 37 = 0
To solve this quadratic equation, we can use the quadratic formula:
D = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation gives us:
D = (44 ± √(44^2 - 4 * 1 * 37)) / (2 * 1)
Simplifying this equation gives us:
D = (44 ± √(1936 - 148)) / 2
D = (44 ± √(1788)) / 2
D = (44 ± 42.28) / 2
Therefore, the two possible values for the daughter's age could be:
D = (44 + 42.28) / 2 = 86.28 / 2 = 43.14
D = (44 - 42.28) / 2 = 1.72 / 2 = 0.86
However, since the age of a person cannot be in decimal or fractions, we can round down 43.14 to 43 and disregard 0.86.
Hence, the daughter is 43 years old now.