The sum of two numbers is 9. Four times the larger number plus three times the smaller number is 48. Find the numbers. Thank you

let the smaller be x

then the larger is 9-x

" Four times the larger number plus three times the smaller number is 48" ---> 4(9-x) + 3x = 48
36 - 4x + 3x = 48
-x = 12
x = -12

The smaller is -12 and the 21

check:
-12 + 21 = 9 , check!
4(21) + 3(-12) = 48 , check!

Well, well, well, looks like we have ourselves a math problem here! Let's give it a go.

Let's call the larger number "x" and the smaller number "y." According to the problem, we have two equations:

Equation 1: x + y = 9
Equation 2: 4x + 3y = 48

Now, let's put on our math hats and solve this!

From Equation 1, we can isolate x by subtracting y from both sides. That gives us: x = 9 - y.

We can plug this value of x into Equation 2, so we have: 4(9 - y) + 3y = 48.

If we simplify that, we get: 36 - 4y + 3y = 48.

Combining like terms, we have: -y = 12.

Dividing both sides by -1, we get: y = -12.

Now that we have y, we can substitute it back into Equation 1 to find x: x + (-12) = 9.

So, x = 21.

Therefore, the larger number is 21 and the smaller number is -12.

Voila! We've solved it. But just remember, numbers don't have feelings, so they won't mind being added or subtracted.

Let's assume the two numbers are x and y.

According to the given information, we have two equations:

Equation 1: x + y = 9 (Sum of the two numbers is 9)
Equation 2: 4x + 3y = 48 (Four times the larger number plus three times the smaller number is 48)

To solve this system of equations, we can use the method of substitution:

Step 1:
Rearrange Equation 1 to solve for x:
x = 9 - y

Step 2:
Substitute the value of x from Step 1 into Equation 2:
4(9 - y) + 3y = 48

Simplifying the equation:
36 - 4y + 3y = 48
36 - y = 48
- y = 48 - 36
- y = 12

Step 3:
Solve for y by multiplying both sides of the equation by -1:
y = -12

Step 4:
Substitute the value of y from Step 3 into Equation 1:
x + (-12) = 9
x - 12 = 9
x = 9 + 12
x = 21

So, the two numbers are x = 21 and y = -12.

To solve this problem, we need to set up a system of equations. Let's call the larger number "x" and the smaller number "y".

From the given information, we have two equations:
- Equation 1: x + y = 9 (since the sum of the two numbers is 9)
- Equation 2: 4x + 3y = 48 (since four times the larger number plus three times the smaller number is 48)

Now we can solve this system of equations by using one of several methods, such as substitution or elimination. Let's solve it using the substitution method.

Step 1: Solve Equation 1 for one variable (x or y). Let's solve it for x:
x = 9 - y

Step 2: Substitute the expression for x in Equation 2:
4(9 - y) + 3y = 48

Step 3: Simplify and solve for y:
36 - 4y + 3y = 48
-y = 12
y = -12

Step 4: Substitute the value of y back into Equation 1 to find x:
x + (-12) = 9
x = 9 + 12
x = 21

So, the larger number is 21 and the smaller number is -12.

Therefore, the two numbers are 21 and -12.