Question

The larger of two numbers is eight more than twice the smaller. The sum of the numbers is 10 less than three times the larger. Find the numbers.

Answer 1

To find the two numbers in question, we set up systems of equations from the given statements, solved for the smaller number first, then used its value to find the larger number. The resulting numbers are -2 for the smaller one and 4 for the larger one.

Step-by-step explanation:

To solve the problem of finding the two numbers, we can set up a system of equations based on the information provided. Let's denote the smaller number as s and the larger number as l.

According to the problem, the larger number is eight more than twice the smaller number, which gives us the first equation:

l = 2s + 8

The sum of the numbers is 10 less than three times the larger, leading to the second equation:

s + l = 3l - 10

Inserting the first equation into the second to solve for s, we get:

s + (2s + 8) = 3(2s + 8) - 10

3s + 8 = 6s + 24 - 10

3s - 6s = 24 - 10 - 8

-3s = 6

s = -2

Having the value of s, we can substitute it back into the first equation to find l:

l = 2(-2) + 8

l = -4 + 8

l = 4

Therefore, the smaller number is -2 and the larger number is 4.

Answer 2

-2 and 4

Step-by-step explanation:

Let's set the larger number to x, and the smaller to y. With these, we can set up our equations.

x = 2y + 8

x + y = 3x - 10

Now, we put the value of x into the second equation.

2y + 8 + y = 3(2y + 8) - 10

Now we can solve for y

3y + 8 = 6y + 24 - 10

3y + 8 = 6y + 14

8 = 3y + 14

-6 = 3y

-2 = y

Now that we have the smaller number, we can put it into the first equation and solve for the larger.

x = 2*-2 + 8

x = -4 + 8

x = 4

So your two numbers are -2 and 4.