Mary's age is 2/3 that of Peter's. Two years ago Mary's age was 1/2 of what Peter's age will be in 5 years time. How old is Peter now? Explain your workings
Let Mary=Y Peter=X
Mary is 2/3 Peter's age therefore:
Y =2/3X
two years ago..mary was 1/2 peter's age in 5 years..we write the equation as:
(Y) -2 = 1/2(x+5)
substitute Y=2/3X
2/3X - 2 = 1/2x + 5/2
solve for X
X=27.....therefore Y=18
Let's assume that Peter's current age is represented by 'P' and Mary's current age is represented by 'M'.
According to the given information:
1) Mary's age is 2/3 that of Peter's, so we have M = (2/3)P.
2) Two years ago, Mary's age was 1/2 of what Peter's age will be in 5 years time. So, we can calculate Mary's age two years ago as M - 2 and Peter's age in 5 years will be P + 5. Therefore, we have the equation M - 2 = (1/2)(P + 5).
Now, let's solve the equations to find the values of P and M.
Substitute the value of M from equation 1 into equation 2:
(2/3)P - 2 = (1/2)(P + 5)
Multiply both sides of the equation by 6 to eliminate the fractions:
4P - 12 = 3(P + 5)
Expand and simplify the equation:
4P - 12 = 3P + 15
4P - 3P = 12 + 15
P = 27
Therefore, Peter's current age is 27 years old.
To solve this problem, we can break it down into steps and use algebraic expressions to represent the ages of Mary and Peter.
Let's assume Peter's current age is x. According to the problem, Mary's age is 2/3 of Peter's age, so we can represent Mary's current age as (2/3)x.
Now, let's consider the second piece of information. Two years ago, Mary's age was 1/2 of what Peter's age will be in 5 years. Two years ago, Mary's age would be (2/3)x - 2, and in 5 years, Peter's age will be x + 5.
So, according to the problem, we have the equation: (2/3)x - 2 = (1/2)(x + 5)
To solve this equation, we will multiply both sides by 6 to eliminate the fractions:
6 * (2/3)x - 6 * 2 = 6 * (1/2)(x + 5)
4x - 12 = 3(x + 5)
Now, distribute the 3 on the right side of the equation:
4x - 12 = 3x + 15
Next, subtract 3x from both sides to get the variables on one side:
4x - 3x - 12 = 15
Simplifying further, we have:
x - 12 = 15
Finally, add 12 to both sides to solve for x:
x = 27
Therefore, Peter is currently 27 years old.