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Component 4C
Sandra is twice as old as Russell. Eight years ago, the product of their ages was 10. Find their current ages.
Q1. Write expressions to show the information in the problem
Q2. Form a trinomial using your expressions from Q1.
Q3. Factorize to solve the problem
Q4. Why is one of the solutions not useable?
Q5. What are the ages of Sandra and Russell?
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Sagot :

DubuChewy

Sandra is twice as old as Russell. Eight years ago, the product of their ages was 10. Find their current ages.

Q1. Write expressions to show the information in the problem

Let S represent Russell's current age. According to the problem:

A. Sandra is twice as old as Russell. Therefore, Sandra's current age is 2S

B. Eight years ago, the product of their ages was 10. Eight years ago, Russell's age was

S−8 and Sandra's age was 2S−8.

Q2. Form a trinomial using your expressions from Q1.

[tex](s−8)(2s−8)=10[/tex]

[tex]2s^{2} −8s−16s+64=10[/tex]

[tex]2s {}^{2} −24s+54=0[/tex]

Q3. Factorize to solve the problem

[tex]s {}^{2} −12s+27[/tex]

To factorize s²-12s+27 , we look for two numbers that multiply to 27 and add up to -12. These numbers are -3 and -9

[tex](s−3)(s−9)=0[/tex]

So,

[tex]s=3 \\ or \\ s=9.[/tex]

Q4. Why is one of the solutions not useable?

To ascertain the correctness of both solutions, we must verify them. Sandra should be twice as old as Russell is, and the product of the ages eight years ago should be ten.

if s = 3 , Russell's current age is 3 and Sandra's current age would be 2s = 2 × 3 = 6

8 years ago

  • Russell's age:

3−8 = − 5 (not possible since age cannot be negative) therefore this solution is not valid

If s = 9

Sandra's current age would be 2s = 2 × 9 = 18

  • Russell's age : 9 - 8 = 1
  • Sandra's age : 18 - 8 = 10
  • The product of 1 × 10 = 10 ( this solution is valid )

Q5. What are the ages of Sandra and Russell?

  • Russell's age is 9 while Sandra's age is 18
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