marleen is 3 years older than Ned and 2 years younger than Carla. 10 years ago Carla's age was equal to the sum of the ages of Ned and Marleen. How old is each now?

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Bethann D. | Mathematics, SAT, and General TutorMathematics, SAT, and General Tutor

Wanda,

To be able to fully answer this question, you must write an equation from the word problem. Be sure to look out for words such as and, less, more, etc. to signify what mathematical symbol (-, +, *, /) you need to use in your equation.

To begin with, let's say that Marleen's age is given by x, since she is the person in the middle. If Marleen=x, then Ned could be represented by three less than x. How would you write that algebraically? Also, if Marleen=x, then Carla would be 2 more than x. How would you write that algebraically?

Hopefully you came up with these answers:

Marleen=x

Ned=x-3

Carla=x+2

From here, we can discuss the second part of the question. If Carla's age ten years ago was equal to the age of Ned and Marleen, how can this be shown in algebraic form?

To start, we know that Carla's age equals something, so Carla= or x+2=

Then, we write what it equals. You should end up with an equation from here.

To solve the equation, use basic algebraic techniques.

If you need help with these techniques, please let me know. Also, make sure that you refer back to the question and find out how old they are now rather than how old they were ten years ago.

Let M=Marleen's age

Marleen is 3 years older than Ned so Ned is 3 years younger than Marleen

Let M-3=Ned's age

Marleen is 2 years younger than Carla so Carla is 2 years older than Marleen

Let M+2=Carla's age

10 years ago means to subtract 10 years from each person's age

M-10=Marleen's age 10 years ago

M-3-10=Ned's age 10 years ago

M+2-10=Carla's age 10 years age

Carla's age=Ned's age + Marleen's age (10 years ago !)

M+2-10=(M-3-10)+(M-10)

M-8=M-13+M-10

M-8=2M-23

23-8=2M-M

15=M, Marleen's age

M-3=15-3=12, Ned's age

M+2=15+2=17, Carla's age

check:15-10=5, 12-10=2, 17-10=7, and 7=5+2

Marleen is 15

Ned is 12

Carla is 17

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