the sum of two numbers is 13 twice the first number added to thrice the second number is 21 find the two numbers
Sure! Let's call the first number x and the second number y. We know that x + y = 13.
Now let's have some fun with math! Twice the first number added to thrice the second number is 21. So, 2x + 3y = 21.
Now, let's solve this puzzle with jokes!
What did the number 7 say to the number 6?
"Nice belt!"
Okay, back to business. We have two equations:
Equation 1: x + y = 13
Equation 2: 2x + 3y = 21
To solve this, I will use a technique called substitution:
From Equation 1, we can express y in terms of x:
y = 13 - x
Now let's substitute this value of y into Equation 2:
2x + 3(13 - x) = 21
2x + 39 - 3x = 21
39 - 21 = 3x - 2x
18 = x
Now, substitute the value of x back into Equation 1:
x + y = 13
18 + y = 13
y = 13 - 18
y = -5
So, the two numbers are 18 and -5.
Why did the number 18 go to the doctor?
Because it wasn't feeling positive!
That's the answer to your question!
Let's assume the first number is represented by "x" and the second number is represented by "y". According to the given information:
1. The sum of two numbers is 13. We can write this as an equation: x + y = 13.
2. Twice the first number added to thrice the second number is 21. We can write this as another equation: 2x + 3y = 21.
To find the values of x and y, we can solve these two equations simultaneously using a method like substitution or elimination. Let's use the method of substitution:
From equation 1, we have x + y = 13, so we can isolate x by subtracting y from both sides: x = 13 - y.
Now substitute x in equation 2 with 13 - y:
2(13 - y) + 3y = 21.
Simplify the equation:
26 - 2y + 3y = 21.
Combine like terms:
y = 21 - 26.
Simplify further:
y = -5.
Now, substitute the value of y back into equation 1:
x + (-5) = 13.
Simplify:
x - 5 = 13.
Add 5 to both sides:
x = 18.
Therefore, the two numbers are x = 18 and y = -5.
To find the two numbers, we can set up a system of equations based on the given information.
Let's assume the two numbers are x and y.
From the given information, we can form two equations:
Equation 1: "The sum of two numbers is 13"
x + y = 13
Equation 2: "Twice the first number added to thrice the second number is 21"
2x + 3y = 21
Now we have a system of equations:
x + y = 13
2x + 3y = 21
To solve this system of equations, we can use substitution or elimination methods. Let's use the substitution method:
Step 1: Solve Equation 1 for x
x = 13 - y
Step 2: Substitute the value of x from Step 1 into Equation 2
2(13 - y) + 3y = 21
Step 3: Simplify and solve for y
26 - 2y + 3y = 21
26 + y = 21
y = 21 - 26
y = -5
Step 4: Substitute the value of y back into Equation 1 to solve for x
x + (-5) = 13
x - 5 = 13
x = 13 + 5
x = 18
The two numbers are x = 18 and y = -5.
Therefore, the solution is x = 18 and y = -5.