Sam's age is five years more than twice Jessica's age. Together, the sum of their ages is 17.
I just did this for 8thgradestudent.
I already answered this in the previous question, but here it is again:
"Sam's age is five years more than twice Jessica's age."
So, Sam's age, which I will designate a "s" is 5 years more than twice Jessica's age, which I will designate as "j".
From this we can realize that twice Jessica's age (2j) plus 5 is equal to Sam's age. From this, we can get the equation:
s = 2j + 5
"Together, the sum of their ages is 17."
This one's pretty straightforward:
s + j = 17
So now we have the system of equations:
s = 2j + 5
s + j = 17
Since we know that s = 2j + 5, we can substitute 2j + 5 for s in the second equation:
s + j = 17
(2j + 5) + j = 17
By using algebra to solve for J in the equation above, you will arrive at the correct answer.
To solve this problem, let's represent Sam's age as "S" and Jessica's age as "J". We are given two pieces of information:
1. Sam's age is five years more than twice Jessica's age: S = 2J + 5
2. The sum of their ages is 17: S + J = 17
Now, we can solve this system of equations using substitution or elimination method.
Let's use the substitution method. We can substitute the value of S from equation 1 into equation 2:
(2J + 5) + J = 17
Now, let's simplify the equation:
3J + 5 = 17
Subtract 5 from both sides of the equation:
3J = 17 - 5
3J = 12
Divide both sides by 3:
J = 4
Now that we know Jessica's age is 4, we can substitute this value back into the equation S = 2J + 5 to find Sam's age:
S = 2(4) + 5
S = 8 + 5
S = 13
Therefore, Jessica's age is 4 and Sam's age is 13.