Samantha is four times as old as Alex now. If Samantha’s age 17 years ago is equal to Alex’s age 13 years from now, how old is Samantha now?
A. 10
B. 20
C. 30
D. 40

Question

Samantha is four times as old as Alex now. If Samantha's age 17 years ago is equal to Alex's age 13 years from now, how old is Samantha now? A. 10 B. 20 C. 30 D. 40

UpStudy AI · Accepted Answer

Let Samantha's current age be $$ S $$ and Alex's current age be $$ A $$.

1. According to the problem, Samantha is four times as old as Alex:
   $$
   S = 4A
   $$

2. The problem also states that Samantha's age 17 years ago equals Alex's age 13 years from now:
   $$
   S - 17 = A + 13
   $$

3. Substitute $$ S = 4A $$ into the second equation:
   $$
   4A - 17 = A + 13
   $$

4. Solve for $$ A $$ by subtracting $$ A $$ from both sides:
   $$
   3A - 17 = 13
   $$

5. Add 17 to both sides:
   $$
   3A = 30
   $$

6. Divide by 3:
   $$
   A = 10
   $$

7. Now, substitute $$ A = 10 $$ back into $$ S = 4A $$:
   $$
   S = 4 \times 10 = 40
   $$

Samantha is $$ \boxed{40} $$ years old now.
Samantha is 40 years old now.

Samantha is four times as old as Alex now. If Samantha’s age 17 years ago is equal to Alex’s age 13 years from now, how old is Samantha now?
A. 10
B. 20
C. 30
D. 40

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Samantha is four times as old as Alex now. If Samantha’s age 17 years ago is equal to Alex’s age 13 years from now, how old is Samantha now? A. 10 B. 20 C. 30 D. 40

Upstudy AI Solution

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Latest Algebra Questions

Samantha is four times as old as Alex now. If Samantha’s age 17 years ago is equal to Alex’s age 13 years from now, how old is Samantha now?
A. 10
B. 20
C. 30
D. 40