3. 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 ___ = _____________
Let ___=______________
Let x = Jack's age
Let y = Malonie's age
Based on the given information, we can set up the following equations:
1) x - y = 4 (Jack is 4 years older than Malonie)
2) x + y = 28 (The sum of their ages is 28)
Solving this system of equations will give us the values of x and y, which represent Jack's and Malonie's ages.
Let x = Jack's age
Let x + 4 = Malonie's age
According to the problem, the sum of their ages is 28:
x + (x + 4) = 28
Simplifying the equation:
2x + 4 = 28
Subtracting 4 from both sides:
2x = 24
Dividing both sides by 2:
x = 12
So Jack is 12 years old, and Malonie is 12 + 4 = 16 years old.
To solve this problem, let's assign variables to represent Jack and Malonie's ages. We can call Jack's age "x" and Malonie's age "y".
Let x = Jack's age
Let y = Malonie's age
According to the problem, Jack and Malonie are 4 years apart in age, so we can write the equation:
x - y = 4
The sum of their ages is 28, so we can also write another equation:
x + y = 28
Now we have a system of two equations with two variables. To find the values of x and y, we can solve this system of equations using a method like substitution, elimination, or graphing. Let's use the method of substitution.
From equation 1, we can isolate x:
x = y + 4
Now substitute this expression for x in equation 2:
(y + 4) + y = 28
Combine like terms:
2y + 4 = 28
Subtract 4 from both sides:
2y = 24
Divide both sides by 2:
y = 12
Substitute the value of y back into equation 1 to find x:
x = 12 + 4
x = 16
So, Jack is 16 years old and Malonie is 12 years old.