One number is 4 more than 3 times another. Four times the larger decreased by 5 times the smaller is equal to the smaller subtracted from 32. Find the numbers.

x = 3y + 4

4x - 5y = 32 - y

Substitute 3y+4 for x in the second equation and solve for y. Insert that value into the first equation to solve for x. Check by putting both values into the second equation.

Well, well, well! Looks like we've got a little math puzzle to solve. Let's break it down step by step, shall we?

Let's call the smaller number "x" and the larger number "y".

According to the problem, we know that one number is 4 more than 3 times the other. So, we can set up the equation:

y = 3x + 4

Now, the problem also tells us that "Four times the larger decreased by 5 times the smaller is equal to the smaller subtracted from 32." In other words:

4y - 5x = 32 - x

Alrighty then! We've got two equations to work with. It's time to put on my math cap and start solving this.

First, let's substitute the value of y from the first equation into the second equation:

4(3x + 4) - 5x = 32 - x

Now it's time to simplify and solve for x:

12x + 16 - 5x = 32 - x
7x + 16 = 32 - x
8x = 16
x = 2

Haha, gotcha there! The smaller number is 2.

Now, let's substitute this value back into the first equation to find the larger number:

y = 3x + 4
y = 3(2) + 4
y = 6 + 4
y = 10

Ta-da! The larger number is 10.

So, the numbers we found are 2 and 10. Hope that math journey brought a smile to your face!

Let's assume the smaller number is x.

According to the given information, the larger number is 4 more than 3 times the smaller number, which can be expressed as (3x + 4).

Now, let's set up the equation based on the second part of the problem statement.

Four times the larger decreased by 5 times the smaller is equal to the smaller subtracted from 32:

4(3x + 4) - 5x = 32 - x

Now, solve this equation step-by-step to find the value of x.

Step 1: Multiply and distribute.

12x + 16 - 5x = 32 - x

Step 2: Combine like terms.

7x + 16 = 32 - x

Step 3: Add x to both sides of the equation.

7x + x + 16 = 32 - x + x

8x + 16 = 32

Step 4: Subtract 16 from both sides of the equation.

8x + 16 - 16 = 32 - 16

8x = 16

Step 5: Divide both sides by 8 to solve for x.

8x/8 = 16/8

x = 2

Now that we have the value of x, we can substitute it back into the equation to find the larger number.

Larger number = 3x + 4
Larger number = 3(2) + 4
Larger number = 6 + 4
Larger number = 10

Therefore, the smaller number is 2 and the larger number is 10.

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

According to the problem, the larger number is 4 more than 3 times the smaller number. We can write this relationship as:
x = 3y + 4

We are also given that four times the larger number decreased by 5 times the smaller number is equal to 32 subtracted from the smaller number. This relationship can be written as:
4x - 5y = 32 - y

Now we have a system of two equations with two variables:
Equation 1: x = 3y + 4
Equation 2: 4x - 5y = 32 - y

To solve this system of equations, we can use substitution or elimination method. Let's use substitution.

Step 1: Substitute the value of x from Equation 1 into Equation 2.
4(3y + 4) - 5y = 32 - y

Step 2: Simplify the equation.
12y + 16 - 5y = 32 - y
7y + 16 = 32 - y

Step 3: Move all the variables to one side and the constant terms to the other side.
7y + y = 32 - 16 - 16
8y = 16

Step 4: Solve for y by dividing both sides by 8.
y = 16 / 8
y = 2

Step 5: Substitute the value of y back into Equation 1 to find x.
x = 3(2) + 4
x = 6 + 4
x = 10

So, the larger number is 10 and the smaller number is 2.