berts age plus twice ernies age is 30. three times berts age plus 8 times ernies age is 108 how old are bert and ernie.
im confused
b + 2 e = 30 so b = (30 - 2 e)
3 b + 8 e = 108
so
3 (30-2e) + 8 e = 108
90 - 6 e +8 e = 108
2 e = 18
e = 9
then b = 30 - 18 = 12
Let's use variables to represent Bert's and Ernie's ages.
Let's say Bert's age is "B" and Ernie's age is "E".
According to the first statement, "Bert's age plus twice Ernie's age is 30":
B + 2E = 30 ----- (Equation 1)
According to the second statement, "three times Bert's age plus 8 times Ernie's age is 108":
3B + 8E = 108 ----- (Equation 2)
Now we have a system of two equations with two variables. We can solve this system using either substitution or elimination.
Let's solve it using elimination:
Multiply Equation 1 by 3:
3(B + 2E) = 3(30)
3B + 6E = 90 ----- (Equation 3)
Subtract Equation 3 from Equation 2:
(3B + 8E) - (3B + 6E) = 108 - 90
3B + 8E - 3B - 6E = 18
2E = 18
E = 9
Now substitute the value of E (9) into Equation 1:
B + 2(9) = 30
B + 18 = 30
B = 30 - 18
B = 12
Therefore, Bert is 12 years old and Ernie is 9 years old.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume Bert's age is "B" and Ernie's age is "E".
According to the first statement, "Bert's age plus twice Ernie's age is 30," we can write the equation as:
B + 2E = 30 (Equation 1)
According to the second statement, "three times Bert's age plus 8 times Ernie's age is 108," we can write the equation as:
3B + 8E = 108 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
From Equation 1, we can express Bert's age (B) in terms of Ernie's age (E):
B = 30 - 2E
Now substitute this value of B into Equation 2:
3(30 - 2E) + 8E = 108
Multiplying and simplifying, we get:
90 - 6E + 8E = 108
Combine like terms:
2E = 18
Divide both sides by 2:
E = 9
Now, we know Ernie's age is 9. We can substitute this value back into Equation 1 to find Bert's age:
B + 2(9) = 30
B + 18 = 30
Subtracting 18 from both sides:
B = 12
Therefore, Bert is 12 years old and Ernie is 9 years old.