a mother is three times as old as her daughter. five years later, the mother will be two and a half times as old as her daughter. Find their present ages.
Now:
daughter --- x
mom ------- 3x
5 years from now:
daughter = x+5
mom = 3x+5
3x+5 = 2.5(x+5)
take over
To find their present ages, let's assign variables to the unknowns. Let's say the daughter's age is "D" and the mother's age is "M."
According to the problem:
1) The mother is three times as old as her daughter: M = 3D.
2) Five years later, the mother will be two and a half times as old as her daughter: (M + 5) = 2.5(D + 5).
Now, let's use these equations to solve for their present ages:
Step 1: Substitute the value of M from equation 1 into equation 2.
(3D + 5) = 2.5(D + 5).
Step 2: Distribute 2.5 on the right side.
3D + 5 = 2.5D + 12.5.
Step 3: Subtract 2.5D from both sides.
3D - 2.5D + 5 = 2.5D - 2.5D + 12.5.
0.5D + 5 = 12.5.
Step 4: Subtract 5 from both sides.
0.5D + 5 - 5 = 12.5 - 5.
0.5D = 7.5.
Step 5: Divide both sides by 0.5 to solve for D.
D = 7.5 / 0.5.
D = 15.
Now that we know the daughter's age is 15, we can find the mother's age using equation 1:
M = 3D = 3 * 15 = 45.
Therefore, the daughter's present age is 15, and the mother's present age is 45.