the sum of two numbers is 21 five times the first number added to 2 times the second number is 66 find the two numbers
8 and 13
Well, it seems like you need my witty mathematical expertise. Let's solve this problem together, shall we?
Let's call the first number 'x' and the second number 'y'.
According to the problem, the sum of the two numbers is 21. So, we can express this as an equation: x + y = 21. And don't worry, these numbers aren't trying to run away from each other, they just want to add up nicely.
The problem also states that five times the first number added to two times the second number is 66. Let's write that down as an equation too: 5x + 2y = 66. That's one fancy math equation right there!
Now, let's use our circus clown tricks to solve this system of equations. We can do that by multiplying the first equation by 5 to match the coefficients of 'x' in both equations. That way, we'll have:
5(x + y) = 5(21) --> 5x + 5y = 105.
Now, we have a system of equations:
5x + 5y = 105 (Equation 1)
5x + 2y = 66 (Equation 2)
To eliminate the '5x' term, let's subtract Equation 2 from Equation 1:
(5x + 5y) - (5x + 2y) = 105 - 66.
After a little bit of calculation, we get:
3y = 39.
Dividing both sides by 3, we find that y = 13. So, the second number is 13. But don't worry; it's not an unlucky number in this equation!
Now, let's substitute the value of y back into one of the original equations. For simplicity, let's use Equation 1:
x + 13 = 21.
Subtracting 13 from both sides, we find that x = 8. The first number is 8. Ta-da!
So, the two numbers are 8 and 13. Now, go forth and rejoice in the joyous world of mathematics!
To find the two numbers, we can set up a system of equations based on the given information.
Let's assume the first number is represented by "x" and the second number is represented by "y".
According to the problem, the sum of two numbers is 21:
Equation 1: x + y = 21
It is also given that five times the first number added to 2 times the second number is 66:
Equation 2: 5x + 2y = 66
Now, we have a system of two equations. We can solve this system using a method called substitution or elimination.
Let's use the substitution method:
Step 1: Solve Equation 1 for x or y.
From Equation 1, we have: x = 21 - y
Step 2: Substitute the value of x in Equation 2.
Substituting x = 21 - y into Equation 2, we get:
5(21 - y) + 2y = 66
Simplify the equation:
105 - 5y + 2y = 66
Combine like terms:
-3y + 105 = 66
Step 3: Solve for y.
Bring the constant term to the other side of the equation:
-3y = 66 - 105
-3y = -39
Divide both sides of the equation by -3:
y = (-39) / (-3)
y = 13
Step 4: Substitute the value of y back into Equation 1 to find x.
x + 13 = 21
Subtract 13 from both sides:
x = 21 - 13
x = 8
Therefore, the two numbers are 8 and 13.
a = first number
b = second number
The sum of two numbers is 21 mean:
a + b = 21
Five times the first number added to 2 times the second number is 66 mean:
5 a + 2 b = 66
a + b = 21 Subtract a to both sides
a + b - a = 21 - a
b = 21 - a
Replace this value in equation:
5 a + 2 b = 66
5 a + 2 ( 21 - a ) = 66
5 a + 2 * 21 - 2 a = 66
5 a + 42 - 2 a = 66
3 a + 42 = 66 Subtactt 42 to both sides
3 a + 42 - 42 = 66 - 42
3 a = 24 Divide both sides by 3
a = 24 / 3 = 8
b = 21 - a = 21 - 8 = 13