Question

5 (a) la différence entre deux nombres est égale à 8. si la somme de ces nombres est égale à 48, quels sont ces nombres?

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \), where \( x > y \). We know that the difference between them is 8, so \( x - y = 8 \), which can be rewritten as \( x = y + 8 \). We also know that their sum is 48, so \( x + y = 48 \).

Step2: Substitute and solve for y

Substitute \( x = y + 8 \) into the sum equation:
\( (y + 8) + y = 48 \)
Simplify the left side:
\( 2y + 8 = 48 \)
Subtract 8 from both sides:
\( 2y = 48 - 8 = 40 \)
Divide both sides by 2:
\( y = \frac{40}{2} = 20 \)

Step3: Solve for x

Now that we know \( y = 20 \), substitute back into \( x = y + 8 \):
\( x = 20 + 8 = 28 \)

Answer:

The two numbers are 28 and 20.