Question

Write two equations:
#1 Jack and his sister, Malonie, are 4 years apart in age.
#2 The sum of their ages is 28.

What are their ages?

let ___ = _____

let ____=_____

Answer 1

Let's define Jack's age as \( J \) and Malonie's age as \( M \).

From the information given, we can write the following equations:

1. \( J - M = 4 \) (Jack is 4 years older than Malonie)
2. \( J + M = 28 \) (The sum of their ages is 28)

Now, we can solve these equations to find their ages.

### Step 1: Rewrite the first equation
From the first equation, we can express \( J \) in terms of \( M \):
\[
J = M + 4
\]

### Step 2: Substitute into the second equation
Now, substitute \( J \) from the first equation into the second equation:
\[
(M + 4) + M = 28
\]
This simplifies to:
\[
2M + 4 = 28
\]

### Step 3: Solve for \( M \)
Subtract 4 from both sides:
\[
2M = 24
\]
Now, divide by 2:
\[
M = 12
\]

### Step 4: Find \( J \)
Now that we have Malonie's age, we can find Jack's age using the first equation:
\[
J = M + 4 = 12 + 4 = 16
\]

So, Jack and Malonie's ages are:
- Jack's age: \( J = 16 \)
- Malonie's age: \( M = 12 \)

In summary:
Let Jack = 16
Let Malonie = 12