Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

1:9. Find the
Ten years ago, the ratio of the age of the father and his son was 11:3. Five
years after the age of father will be 10 years older than two times the age of
his son. Find after how many years the age of the son will be equal to the
present age of his father.

Sagot :

GinnyAnswer
Certainly! Let's break down the problem step-by-step:

1. Understand the Problem:
- Ten years ago, the ratio of the father's age to the son's age was 11:3.
- Five years from now, the father's age will be 10 years older than twice the son's age at that time.
- We need to determine after how many years the son's age will be equal to the present age of his father.

2. Setup Variables:
- Let [tex]\( F \)[/tex] be the father's age 10 years ago.
- Let [tex]\( S \)[/tex] be the son's age 10 years ago.

3. Establish Equations Using Given Conditions:

Condition 1: Ratio of Ages 10 Years Ago
- According to the problem, 10 years ago the ratio of the father's age to the son's age was [tex]\( \frac{F}{S} = \frac{11}{3} \)[/tex].
- This gives us the equation:
[tex]\[ F = \frac{11}{3}S \][/tex]

Condition 2: Age Relationship 5 Years From Now
- Five years after 10 years later (15 years from the ages we considered initially), the father's age will be 10 years older than twice the son's age.
- This gives us the equation:
[tex]\[ F + 15 = 2(S + 15) + 10 \][/tex]

4. Solve the Equations Simultaneously:
Solve the system of equations given:
[tex]\[ F = \frac{11}{3}S \][/tex]
[tex]\[ F + 15 = 2S + 40 \][/tex]

Substituting [tex]\( F \)[/tex] from the first equation into the second equation:
[tex]\[ \frac{11}{3}S + 15 = 2S + 40 \][/tex]

Clear the fraction by multiplying all terms by 3:
[tex]\[ 11S + 45 = 6S + 120 \][/tex]

Simplify and solve for [tex]\( S \)[/tex]:
[tex]\[ 11S - 6S = 120 - 45 \][/tex]
[tex]\[ 5S = 75 \][/tex]
[tex]\[ S = 15 \][/tex]

Now, find [tex]\( F \)[/tex]:
[tex]\[ F = \frac{11}{3} \times 15 \][/tex]
[tex]\[ F = 55 \][/tex]

5. Find the Current Ages:
- Since these ages are from 10 years ago, we add 10 years to both.
- Current age of father [tex]\( = F + 10 = 55 + 10 = 65 \)[/tex].
- Current age of son [tex]\( = S + 10 = 15 + 10 = 25 \)[/tex].

6. Determine After How Many Years the Son's Age Will Equal the Father's Current Age:
- We want to find [tex]\( x \)[/tex] such that the son's age + [tex]\( x \)[/tex] years equals the father's current age.
- Set up the equation:
[tex]\[ 25 + x = 65 \][/tex]

Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 65 - 25 \][/tex]
[tex]\[ x = 40 \][/tex]

Therefore, the son will be equal to the present age of his father after 40 years.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.