Answer:
Pamela is 30 years old.
Explanation:
- We can find Pamela's age using a system of equations where P represents Pamela's age and J represents Jakob's.
First equation:
Since Pamela is 3 times older than Jakob, our first equation is given by:
P = 3J
Second Equation:
Since Pamela will be twice as old as Jakob in 10 years, our second equation is given by:
P = 2J + 10
Method to solve: Substitution:
We can solve with substitution by isolating J in the second equation. This will allow us to substitute it for J in the second equation and find P, Pamela's age:
Isolating J:
Step 1: Divide both sides by 3
(P = 3J) / 3
P/3 = J
Substituting P/3 = J for J in P = 2J + 10:
P = 2(P/3) + 10
Step 1: Distribute the 2 to P/3:
P = 2/3P + 10
Step 2: Multiply both sides by 3 to clear the fraction:
(P = 2/3P + 10) * 3
3P = 2P + 30
Step 3: Subtract 2P from both sides:
(3P = 2P + 30) - 2P
P = 30
Step 4: Divide both sides by 2 to find P, Pamela's age:
(2P = 30) / 2
P = 30
Thus, Pamela is 30 years old.
Optional Steps to check the validity of our answer:
- In order to check that our answers for Pamela's age is correct, we will first need to find Jakob's age by plugging in 30 for P in any of the two equations in our system.
- Let's use the first one:
Plugging in 30 for P in P = 3J:
Step 1: Divide both sides by 3:
(30 = 3J) / 3
10 = J
Thus, Jakob is 10 years old.
Checking the validity of answers with verbal statements:
Since 30 (i.e., Pamela's age) is indeed 3 times 10 (i.e., Jakob's age), this satisfies the first statement.
In 10 years, Pamela will be 40 as 30 + 10 = 40.
In 10 years, Jacob will be 20 as 10 + 10 = 20.
Since 40 (i.e., Pamela's age in 10 years) is indeed twice 20 (i.e., Jakob's age in 10 years), this satisfies the second statement.
Thus, our answer for Pamela's age is correct.