10 yrs ago, Jane was 4 times as old as bianca. Now she is only twice as old as Bianca. Find their present age
bianca 10 and jane is 20
j-10 = 4(b-10)
j = 2b
now it's a cinch, right?
To find Jane and Bianca's present age, let's first assign variables to their ages.
Let's say Jane's present age is J and Bianca's present age is B.
According to the given information, 10 years ago:
Jane's age was J - 10, and Bianca's age was B - 10.
Jane was also 4 times as old as Bianca, so we can write an equation:
J - 10 = 4(B - 10).
Now, let's consider their present ages:
Jane's present age is J, and Bianca's present age is B.
The second piece of information states that Jane is now only twice as old as Bianca, so we can write another equation:
J = 2B.
We have a system of two equations:
J - 10 = 4(B - 10), and J = 2B.
Now, we can solve this system of equations to find the values of J and B.
From the second equation, we have J = 2B.
Substitute this value of J into the first equation:
2B - 10 = 4(B - 10).
Simplify:
2B - 10 = 4B - 40.
Subtract 2B from both sides:
-10 = 2B - 40.
Add 40 to both sides:
30 = 2B.
Divide both sides by 2:
B = 15.
Now substitute this value of B back into the second equation:
J = 2(15),
J = 30.
Therefore, Jane's present age is 30, and Bianca's present age is 15.