fifteen years ago Jane was x years old, and also Karen was one third(1/3) as old as Jane.
a) Write down an algebraic expression for Karen's age fifteen years ago, in terms of x.
- would it be x/3
b) write down an algebraic expression for Karen's age now, in terms of x
- would it be (x + 15) / 3
c) write down an algebraic expression for Jane's age now in terms of x
d) Now Karen is three quarters(3/4) as old as Jane. Write down an expression and solve for x.
e) How old is Jane
I am finding hard to work these out
a) correct
b) x/3 + 15
c) x+15
d) x/3 + 15 = 3/4 (x+15)
x = 9
e) Jane = x+15 = 24
Check:
Karen is 3/4 * 24 = 18
15 years ago, she was 3, or 1/3 of 9
c) To write down an algebraic expression for Jane's age now in terms of x, we need to consider that fifteen years have passed since Jane was x years old. So, Jane's age now would be x + 15.
d) To write down an algebraic expression for Karen's age now in terms of x, we know that Karen is currently three quarters (3/4) as old as Jane. Therefore, Karen's age now would be (3/4) * (x + 15).
Now, to solve for x, we can equate Karen's age to Jane's age:
(3/4) * (x + 15) = x + 15
First, let's distribute:
(3/4) * x + (3/4) * 15 = x + 15
Next, let's simplify by multiplying:
(3/4) * x + 45/4 = x + 15
Now, let's move all terms with x to one side of the equation and all constant terms to the other side:
(3/4) * x - x = 15 - 45/4
Now, let's find a common denominator and subtract:
(3/4) * x - (4/4) * x = 60/4 - 45/4
Simplifying:
(3/4 - 4/4) * x = 15/4
(-1/4) * x = 15/4
Now, let's isolate x by multiplying both sides by -4:
x = -15/1
Therefore, x = -15.
e) Since we have found the value of x to be -15, we can substitute this value into Jane's age expression, x + 15, to find Jane's age:
Jane's age = -15 + 15 = 0 years old.
Therefore, Jane is currently 0 years old.