Cassandra is two thirds as old as Jeremy. Three years ago she was half as old as Jeremy. How old are Cassandra and Jeremy?
I got this question wrong and was wondering what I did wrong. This is what I did.
Now 3 years ago
Cassandra| C | C-3
Jeremy | J | J-3
C=2/3J
C-3=1/2(J-3)
(C-3=1/2J-3/2) x 2
2C-6=J-3
2(2/3J)-6=j-3
4/3J-6=J-3
3 x (4/3J -6=J-3)
4J-18=J-9
+18 +18
4J=J+9
-J -J
3J=9 Divide everything by 3
J=3
C=2/3(3)
C=2
Jeremy is 3 years old
Cassandra is 2 years old
Oh I think I know what I did wrong now
j three fourth as old as m in 20 years j will be seven eight as old as m how old is each now
Your approach to solving the problem is mostly correct, but there is a small mistake in your calculation. Let's go through the problem and the correct calculation step by step.
Given:
Cassandra is two-thirds as old as Jeremy.
Three years ago, Cassandra was half as old as Jeremy.
Let's start by assigning variables to their ages:
Let J represent Jeremy's current age.
Let C represent Cassandra's current age.
From the given information, we can write two equations:
1) Cassandra is two-thirds as old as Jeremy:
C = (2/3)J
2) Three years ago, Cassandra was half as old as Jeremy:
C - 3 = (1/2)(J - 3)
Now let's solve these equations:
Equation 1:
C = (2/3)J
Equation 2:
C - 3 = (1/2)(J - 3)
Expanding the right side:
C - 3 = (1/2)J - 3/2
Multiply both sides of Equation 2 by 2 to eliminate the fraction:
2(C - 3) = J - 3
2C - 6 = J - 3
Rearranging:
2C = J + 3
Now we have a system of equations:
C = (2/3)J
2C = J + 3
We can solve this system by substitution or elimination.
Using substitution method:
Substitute the value of C from the first equation into the second equation:
2((2/3)J) = J + 3
(4/3)J = J + 3
Multiply both sides by 3 to eliminate the fraction:
4J = 3J + 9
Subtract 3J from both sides:
4J - 3J = 9
J = 9
Now we know Jeremy's age is 9.
Substitute this value back into the first equation to find Cassandra's age:
C = (2/3)J
C = (2/3)(9)
C = 6
So Jeremy is 9 years old and Cassandra is 6 years old.
In your calculation, you made a small mistake when simplifying 2(2/3J) - 6. The correct simplification is 4/3J - 6, not 4J - 6. This mistake led to the incorrect equation 4J - 18 = J - 9.