The sum of 6 times Jack's age and 5 times Larry's age is 63. Jack is 1 year less than 3 times as old as Larry. Find eachh of their ages.
6J+5L=63
J+1=3L
Let's represent Jack's age as "J" and Larry's age as "L".
According to the given information, we can set up two equations:
1) 6J + 5L = 63 (equation 1) (the sum of 6 times Jack's age and 5 times Larry's age is 63)
2) J = 3L - 1 (equation 2) (Jack is 1 year less than 3 times as old as Larry)
From equation 2, we can express J in terms of L:
J = 3L - 1
Substituting this expression into equation 1, we get:
6(3L - 1) + 5L = 63
Simplifying the left side:
18L - 6 + 5L = 63
Combining like terms:
23L - 6 = 63
Adding 6 to both sides:
23L = 69
Now, divide both sides by 23:
L = 3
Substituting this value back into equation 2 to find J:
J = 3L - 1
J = 3(3) - 1
J = 9 - 1
J = 8
Therefore, Jack is 8 years old and Larry is 3 years old.
To solve this problem, we need to translate the given information into equations and then solve the system of equations.
Let's denote Jack's age as J and Larry's age as L.
According to the first statement, the sum of 6 times Jack's age and 5 times Larry's age is 63. So we can write the equation as:
6J + 5L = 63 (Equation 1)
According to the second statement, Jack's age is 1 year less than 3 times Larry's age. We can write this as:
J = 3L - 1 (Equation 2)
Now we have a system of two equations with two variables. We can solve this system using substitution or elimination method.
Let's use substitution method:
Substitute the value of J from Equation 2 into Equation 1:
6(3L - 1) + 5L = 63
Simplify the equation:
18L - 6 + 5L = 63
Combine like terms:
23L - 6 = 63
Add 6 to both sides:
23L = 69
Divide both sides by 23:
L = 3
Now substitute the value of L back into Equation 2 to find J:
J = 3(3) - 1
J = 9 - 1
J = 8
Therefore, Jack is 8 years old and Larry is 3 years old.