One number is 5 more than the other. Their sum is 33. Find the numbers.
who said anything about 3 times?
x + (x+5) = 33
Let's call the first number x and the second number y.
According to the problem, one number is 5 more than the other, so we can write the equation:
x = y + 5 ----- (Equation 1)
It is also given that their sum is 33, so we can write the second equation:
x + y = 33 ----- (Equation 2)
Now, we can solve the system of equations by substituting equation 1 into equation 2:
(y + 5) + y = 33
Combining like terms:
2y + 5 = 33
Subtracting 5 from both sides:
2y = 28
Dividing both sides by 2:
y = 14
Now, substitute the value of y into equation 1:
x = y + 5
x = 14 + 5
x = 19
So, the two numbers are 19 and 14.
To solve this problem, we can set up a system of equations based on the given information:
Let's call the first number x, and the second number y.
The problem states that one number is 5 more than the other, so we can express this relationship as:
x = y + 5 (Equation 1)
The problem also states that their sum is 33, which we can express as:
x + y = 33 (Equation 2)
Now we have a system of two equations with two variables. We can solve it using the substitution or elimination method.
Substitution Method:
From Equation 1, we know that x = y + 5. We can substitute this value into Equation 2:
(y + 5) + y = 33
2y + 5 = 33
Next, we can isolate y by subtracting 5 from both sides of the equation:
2y = 33 - 5
2y = 28
Then, divide both sides of the equation by 2 to solve for y:
y = 28 / 2
y = 14
Now that we have the value of y, we can substitute it back into Equation 1 to find x:
x = y + 5
x = 14 + 5
x = 19
Therefore, the two numbers are 19 and 14.
Using the elimination method or any other equivalent method would lead to the same result.
x + (3x + 5) = 29
4x + 5 = 29
4x = 24
X=6
So the two numbers are 6 and 3*6+5 = 23