Question

1. the difference between two numbers is 2. if 3 times the larger plus 5 times the smaller is 94, what are the numbers?

Explanation:

Step1: Define Variables

Let the larger number be \( x \) and the smaller number be \( y \). The difference between the two numbers is 2, so \( x - y = 2 \), which can be rewritten as \( x = y + 2 \).

Step2: Set Up the Second Equation

3 times the larger plus 5 times the smaller is 94, so \( 3x + 5y = 94 \).

Step3: Substitute \( x \) into the Second Equation

Substitute \( x = y + 2 \) into \( 3x + 5y = 94 \):
\( 3(y + 2) + 5y = 94 \)
Expand the left side: \( 3y + 6 + 5y = 94 \)
Combine like terms: \( 8y + 6 = 94 \)
Subtract 6 from both sides: \( 8y = 94 - 6 = 88 \)
Divide both sides by 8: \( y = \frac{88}{8} = 11 \)

Step4: Find \( x \)

Substitute \( y = 11 \) into \( x = y + 2 \): \( x = 11 + 2 = 13 \)

Answer:

The two numbers are 13 and 11.