Question

The larger of two numbers is 6 more than 3 times the smaller. If the twice the larger number is increased by 3 times the smaller, the result is 3. Find the numbers by solving algebraically. Show your work including the equations.

Answer 1

The smaller number = -1

The larger number = 3

Explanation:

Let the smaller number = a

Let the larger number = b

The larger of two numbers is 6 more than 3 times the smaller.

b = 3a + 6........... Equation 1

If the twice the larger number is increased by 3 times the smaller, the result is 3.

2b + 3a = 3........ Equation 2

Hence:

We Substitute 3a + 6 for b in Equation 2

2b + 3a = 3

2(3a + 6) + 3a = 3

6a + 12 + 3a = 3

9a = 3 - 12

9a = -9

a = -9/9

a = -1

b = 3a + 6........... Equation 1

b = 3(-1) + 6

b = -3+ 6

b = 3

Therefore,

The smaller number = -1

The larger number = 3