Question

A number is 5 more than three times the other number. Twelve less than four times the smaller number equals

three times the greater number. Find the numbers.
O 11.2 and -5.4
O -5.4 and -11.2
O -11.2 and 5.4
O 5.4 and 11.2

Answer 1

Answer: -5.4 and -11.2

Step-by-step explanation: To find the numbers, let's represent the smaller number as x and the greater number as y.

According to the problem, we can create two equations based on the given information:

1. "A number is 5 more than three times the other number":

y = 3x + 5

2. "Twelve less than four times the smaller number equals three times the greater number":

4x - 12 = 3y

Now, we can solve this system of equations to find the values of x and y.

Let's start by substituting the value of y from the first equation into the second equation:

4x - 12 = 3(3x + 5)

expanding the equation:

4x - 12 = 9x + 15

Moving the variables to one side and the constants to the other side:

4x - 9x = 15 + 12

Simplifying the equation:

-5x = 27

Dividing both sides by -5:

x = -5.4

Now, we can substitute this value back into the first equation to find y:

y = 3(-5.4) + 5

y = -16.2 + 5

y = -11.2