Raymonds age plus his sister janice's age is 48 years. Janice's age is half Raymonds age plus six years. How old is Raymond? How old is janice
Let's solve the equation step-by-step to find the ages of Raymond and Janice.
Step 1: Let's assign variables to the unknown ages. Let's say Raymond's age is R, and Janice's age is J.
Step 2: According to the given information, the sum of Raymond's age and Janice's age is 48 years. This can be written as:
R + J = 48 ---(Equation 1)
Step 3: It is also given that Janice's age is half Raymond's age plus six years. We can write this as:
J = (R / 2) + 6 ---(Equation 2)
Step 4: Now, we have a system of equations with two unknowns. We can solve this system by substituting Equation 2 into Equation 1.
Substituting (R / 2) + 6 for J in Equation 1, we get:
R + (R / 2) + 6 = 48
Step 5: Simplifying the equation:
(3R / 2) + 6 = 48
Subtracting 6 from both sides, we get:
(3R / 2) = 42
Step 6: To get rid of the fraction, we can multiply both sides of the equation by 2:
2 * (3R / 2) = 2 * 42
3R = 84
Step 7: Dividing both sides of the equation by 3, we get:
R = 28
Step 8: Now that we have found Raymond's age, we can substitute it back into Equation 2 to find Janice's age:
J = (28 / 2) + 6
Simplifying the equation, we get:
J = 14 + 6
J = 20
So, Raymond is 28 years old, and Janice is 20 years old.
To determine the ages of Raymond and Janice, we can set up two equations based on the given information.
Let's assign variables to represent their ages:
Raymond's age = R
Janice's age = J
Based on the first statement, we know that Raymond and Janice's ages add up to 48 years:
Equation 1: R + J = 48
According to the second statement, Janice's age is half Raymond's age plus six:
Equation 2: J = (R / 2) + 6
To solve this system of equations, we will substitute Equation 2 into Equation 1:
(R / 2) + 6 + R = 48
To get rid of the fraction, multiply every term in the equation by 2:
2 * [(R / 2) + 6] + 2R = 2 * 48
R + 12 + 2R = 96
3R + 12 = 96
Subtract 12 from both sides:
3R = 96 - 12
3R = 84
Divide both sides by 3 to isolate R:
R = 84 / 3
R = 28
Now that we know Raymond's age is 28, we can substitute this value back into Equation 1 to find Janice's age:
28 + J = 48
J = 48 - 28
J = 20
Therefore, Raymond is 28 years old, and Janice is 20 years old.
R + J = 48
J = .5 R + 6
R + (.5 R + 6) = 48
1.5 R = 42 etc