Total age of 3 sisters is 39
Dina is 1/2 as old as Michelle and 3 years younger than Juliettte.
How old are the sisters ?
D+M+J=39
D=1/2 M
D=J+3
and, M=2D
J=D-3
intothe first equation
D+2D+D-3=39
4d=36
you take if from here.
To solve this problem, let's start by assigning variables to represent the ages of the sisters.
Let:
D = Dina's age
M = Michelle's age
J = Juliette's age
Given that the total age of the three sisters is 39, we can write the equation:
D + M + J = 39 (equation 1)
We are also given that Dina is 1/2 as old as Michelle, so we can write the equation:
D = 1/2 * M (equation 2)
And finally, we know that Dina is 3 years younger than Juliette, so we can write the equation:
D = J - 3 (equation 3)
Now we have a system of three equations. To solve this system, we'll use a method called substitution.
Starting with equation 2, substitute the value of D in terms of M from equation 3 into equation 1:
1/2 * M + M + J = 39
Now, let's simplify this equation:
3/2 * M + J = 39
Next, substitute the value of D in terms of J from equation 3 into equation 2:
J - 3 = 1/2 * M
Multiply both sides of the equation by 2 to eliminate fractions:
2J - 6 = M
Now we have a system of two equations:
3/2 * M + J = 39 (equation 4)
2J - 6 = M (equation 5)
To solve this system, we'll use the method of substitution again. Solve equation 5 for M:
M = 2J - 6 (equation 6)
Substitute the value of M from equation 6 into equation 4:
3/2 * (2J - 6) + J = 39
Simplify this equation:
3J - 9 + J = 39
Combine like terms:
4J - 9 = 39
Add 9 to both sides of the equation:
4J = 48
Divide both sides of the equation by 4:
J = 12
Substitute the value of J back into equation 6 to find M:
M = 2(12) - 6
M = 24 - 6
M = 18
Finally, substitute the values of M and J into equation 3 to find D:
D = J - 3
D = 12 - 3
D = 9
Therefore, the ages of the sisters are:
Dina is 9 years old,
Michelle is 18 years old, and
Juliette is 12 years old.