Find Kari & Jackie's Ages: 2C-13+1C=66

  • Context: MHB 
  • Thread starter Thread starter DawnC
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Discussion Overview

The discussion revolves around a problem involving the ages of two individuals, Kari and Jackie, where Kari's age is defined in relation to Jackie's age. Participants are working through the algebraic setup and solution of the problem, which involves determining their ages based on given conditions.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Technical explanation

Main Points Raised

  • Participants establish the relationship between Kari's age and Jackie's age, with Kari's age being defined as 13 less than twice Jackie's age.
  • There is a discussion about setting up the equation correctly, with some participants confirming that the equation should be written as 2C - 13 + 1C = 66.
  • One participant suggests the next steps in solving the equation, indicating a process of combining like terms and isolating the variable C.
  • Concerns are raised about whether the numbers 13 and 66 are part of the original problem, with one participant noting that the ages may not yield integer solutions.
  • Another participant questions the necessity of integer solutions for age problems, while others assert that most age problems typically involve integers.
  • One participant provides a structured approach to solving the problem, outlining the equations for both ages and suggesting a method for finding the solution.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of integer solutions for age problems. While some assert that ages should typically be integers, others question this assumption. The discussion remains unresolved regarding the implications of non-integer solutions.

Contextual Notes

There is an assumption that the problem is correctly stated, but the potential for confusion exists regarding the integer nature of the solutions. The discussion also reflects varying levels of familiarity with algebraic problem-solving among participants.

DawnC
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Age question:

Kari's age is 13 less than twice Jackie's age, C. If the sum of their age is 66, find each person's age.

2c-13 = Kari
1C = Jackie

Would I sent up this question as 2C-13+1C = 66?
 
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DawnC said:
Age question:

Kari's age is 13 less than twice Jackie's age, C. If the sum of their age is 66, find each person's age.

2C-13 = Kari
1C = Jackie

Would I sent up this question as 2C-13+1C = 66?

Yes, that's correct. Now you can determine both ages. :D
 
Would the next step then be?

2c -13 +1c = 3c -13 = 66 then minus 66-13?
 
DawnC said:
Would the next step then be?

2c -13 +1c = 3c -13 = 66 then minus 66-13?

You want to remain consistent with your variable names...you began with $C$ (uppercase), so let's stick with that:

$$2C-13+C=66$$

So, yes, now combine like terms on the left:

$$3C-13=66$$

Now, our ultimate goal here is to isolate $C$ on the left, and since 13 is being subtracted on the left, how can we undo this subtraction while still maintaining the equality of both sides of the equation?
 
DawnC said:
Kari's age is 13 less than twice Jackie's age, C. If the sum of their age is 66,
Are you sure 13 and 66 are both in original problem?
As is, ages are not integers...
 
Wilmer said:
Are you sure 13 and 66 are both in original problem?
As is, ages are not integers...

Do they have to be? :D
 
Bacterius said:
Do they have to be? :D
Of course not; however, 99.9% of age problems are,
and more so in this case as the student is apparently a beginner.
 
DawnC said:
Age question:

Kari's age is 13 less than twice Jackie's age, C. If the sum of their age is 66, find each person's age.

2c-13 = Kari
1C = Jackie

Would I sent up this question as 2C-13+1C = 66?
According to the question,
Age of Jackie = $c$
Age of Kari = $2c-13 \tag{1}$
Sum of their ages = $c+(2c-13)=66 \tag{2}$
Solving (2) will give you the value of $c$ (age of Jackie).
Substituting the value of $c$ in (1) will give you the age of Kari.

Where are you getting confused?
 

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