Write the equations: Jack and his sister Malonie are 4 years apart in age. The sum of their ages is 28. What are their ages?
Let J be Jack's age and M be Malonie's age. We can express the problem as a system of equations:
J - M = 4 (Jack and Malonie are 4 years apart in age)
J + M = 28 (The sum of their ages is 28)
To solve this system, we can use the method of substitution. We solve the first equation for J: J = M + 4.
We substitute this into the second equation: (M + 4) + M = 28.
Combining like terms: 2M + 4 = 28.
Subtracting 4 from both sides: 2M = 24.
Dividing both sides by 2: M = 12.
Substituting this value back into the first equation: J - 12 = 4.
Adding 12 to both sides: J = 16.
Therefore, Jack is 16 years old and Malonie is 12 years old.