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Lauren’s age is 2/3 of kylie’s age. Twelve years ago, Lauren’s age was half of Kylie’s age. How old is Lauren now?

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3 Answers

If you have learned pre-algebra and algebra, you can use linear equation 3/2 X-12=2(X-12) to easily solve the variable . If you haven't learned algebra, you can get the answer by drawing a graph:

Lauren's age is 2/3 of Kylie's age, you can draw a graph to represent Kyile and Lauren's age as below. (Kyile has 3 units of age, Lauren has 2 units of age.)

Kylie    I------------I------------I------------I

Lauren I------------I------------I


12 years ago, Lauren's age was half of Kyile's age. Hence, Lauren's age -12 = 1/2 (Kyile's age -12).

If you double Lauren's age, then minus twice the number 12, it will equal to Kyile's age minus 12. 

Thus 2xLauren's age is 12 years more than Kyile's age. 

Adding that information on the graph:  

Kylie      I------------I------------I------------I


2Lauren I------------I------------I------------I------------I


                                                            I      12     I

2Lauren has 4 units of age, kylie has 3 units of age. Hence one unit equals to 12.

Lauren's age is two units of age: 2x12=24




Quick way:

Let 2x = Lauren’s age, thus 3x = Kylie’s age

12 years ago, 2(2x-12) = 3x-12

Solve for x,

x = 12

Therefore, Lauren's age is 24 years old, and Kylie's age is 36 years old.

It is helpful to use variables to represent either the current or original ages of Kylie and Lauren.

Let's say their current ages are K (Kylie) and L (Lauren). Then The first statement translates to L=(2/3)*K.

Let's look at the other statement. Their ages 12 years ago were K-12 and L-12. Makes sense? They were each twelve years younger then.

Since Lauren was half as old, we can see that L-12 = (1/2)*(K-12). We can now solve the system of two linear equations.

Plugging in L = (2/3)K into the second equation will give us:

(2/3)K - 12 = (1/2)*(K-12)

                 = (1/2)K - 6 (Distributive Property)

Subtracting (1/2)K from both sides gives:

(1/6)K - 12 = -6

Adding 12 to both sides gives:

(1/6)K = 12-6 = 6

So K = 6*(1/6)K = 6*6 = 36.

So L = (2/3)*36 = 24