the larger of the two numbers is 8 more than twice the smaller. The sum of the numbers is 10 less than three time the larger. Find the numbers

smaller ---- x

larger ------y

"the larger of the two numbers is 8 more than twice the smaller" ---> y = 2x+8

" The sum of the numbers is 10 less than three time the larger" ---> x+y = 3y - 10

Notice I literally translate the English into Math

sub the first into the second ...
x + (2x+8) = 3(2x+8) - 10
x + 2x + 8 = 6x + 24 - 10
-3x = 6
x = -2
then y = -4+8 = 4

the smaller is -2 and the larger is 4

Well, I must say, these numbers seem to be quite mischievous! Let's call the smaller number "x" and the larger number "y". According to the information given, we can write two equations:

1. y = 2x + 8 (The larger number is 8 more than twice the smaller)

2. x + y = 3y - 10 (The sum of the numbers is 10 less than three times the larger)

Now, let's solve this little math puzzle with some humor-packed calculations!

From equation 1, let's isolate x:
x = (y - 8) / 2

Now, substitute this value of x into equation 2:
(y - 8) / 2 + y = 3y - 10

To make things easier, let's multiply everything by 2 to get rid of that pesky fraction:
y - 8 + 2y = 6y - 20

Bring all the y's to one side and constants to the other:
y + 2y - 6y = 8 - 20
-3y = -12

Divide both sides by -3 to isolate y:
y = (-12) / (-3)
y = 4

Now substitute this value of y back into equation 1:
x = 2(4) + 8
x = 8 + 8
x = 16

So, the two mischievous numbers are 16 and 4. Watch out, these numbers definitely know how to play tricks!

Let's assume the smaller number as x and the larger number as y.

According to the given information:
1. The larger number is 8 more than twice the smaller:
y = 2x + 8

2. The sum of the numbers is 10 less than three times the larger:
x + y = 3y - 10

Now we can solve these two equations simultaneously to find the values of x and y.

Substituting the value of y from the first equation into the second equation:
x + (2x + 8) = 3(2x + 8) - 10

Simplifying the equation:
x + 2x + 8 = 6x + 24 - 10
3x + 8 = 6x + 14

Bringing like terms together:
3x - 6x = 14 - 8
-3x = 6

Dividing both sides by -3:
x = -2

Substituting the value of x back into the first equation:
y = 2(-2) + 8
y = -4 + 8
y = 4

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

To solve this problem, let's assign variables to the two numbers. Let's call the larger number L and the smaller number S.

According to the given information:
1. The larger number is 8 more than twice the smaller, so we can write L = 2S + 8.
2. The sum of the numbers is 10 less than three times the larger, so we can write L + S = 3L - 10.

Now, we have a system of two equations:
Equation 1: L = 2S + 8
Equation 2: L + S = 3L - 10

To solve this system, we can substitute Equation 1 into Equation 2:
(2S + 8) + S = 3(2S + 8) - 10
Simplifying this equation:
3S + 8 = 6S + 24 - 10
Combine like terms:
3S + 8 = 6S + 14
Subtract 3S from both sides:
8 = 3S + 14
Subtract 14 from both sides:
-6 = 3S
Divide by 3 on both sides:
S = -2

Now that we have the value of S, we can substitute it back into Equation 1 to find L:
L = 2(-2) + 8
L = -4 + 8
L = 4

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