At present, the ratio of Ann's age to Pamela's age is 4:3. Six yrs ago, their total age was 72yrs. what is Pamela's presnt age?
let Ann's age be 4x
let Pam's age be 3x , notice the raio of their ages will be 4:3
six yrs ago
Ann: 4x-6
Pam: 3x-6
4x-6 + 3x-6 = 72
solve for x, easy from there
To find Pamela's present age, let's start by assigning variables to the ages of Ann and Pamela.
Let A represent Ann's present age.
Let P represent Pamela's present age.
According to the given information, the ratio of Ann's age to Pamela's age is 4:3. This can be written as:
A/P = 4/3
Next, we are told that six years ago, their total age was 72 years. So, we can set up an equation based on this statement:
(A - 6) + (P - 6) = 72
Now we have two equations:
Equation 1: A/P = 4/3
Equation 2: (A - 6) + (P - 6) = 72
To solve this system of equations, we can use a method called substitution.
From Equation 1, we can isolate A by multiplying both sides of the equation by P:
A = (4/3)P
Now we substitute this expression for A in Equation 2:
((4/3)P - 6) + (P - 6) = 72
To simplify, let's convert the fraction (4/3) to an improper fraction:
A common denominator for P and 3 is 3P, so the equation becomes:
(4P - 18 + 3P - 18)/3P = 72
Simplifying further:
(7P - 36)/3P = 72
Now, cross-multiply:
7P - 36 = 72 * 3P
Simplify again:
7P - 36 = 216P
Rearrange the equation:
216P - 7P = 36
Combine like terms:
209P = 36
Finally, divide both sides of the equation by 209 to solve for P:
P = 36/209
Therefore, Pamela's present age is approximately 0.172 years (about 2 months), according to the calculations.