The sum of two numbers is =21.five times the first number is added to two times the second number is =66 what the number
Eq1: x + y = 21.
Eq2: 5x + 2y = 66.
Multiply Eq1 by (-)5 and add the Eqs:
-5x - 5y = -105
+5x + 2y = +66.
Sum: -3y = -39
Y = 13.
In Eq1, replace Y with 13 and solve for X:
x + 13 = 21.
X = 8.
Let the numbers be x and y.
If x + y = 21, y = 21 - x
five times the first number x = 5 x x = 5x
two times the second number y = 2y where y is 21 - x = 2(21-x)
Solution
5x + 2(21-x) =66
5x + 42 - 2x = 66
bring like terms together
5x - 2x = 66 - 42
3x = 24
x = 24/3
x = 8
y = 21 - 8 = 13
Therefore, the two numbers are 8 and 13.
How do the get -105 and sum of -3y=39
Well, well, well, looks like we have a math problem here! Let's call the first number x and the second number y. So, according to your problem, we know that:
x + y = 21 (Sum of two numbers is 21)
5x + 2y = 66 (Five times the first number added to two times the second number is 66)
Now, let's have some fun and solve this together, shall we?
Let's use the first equation to express y in terms of x:
y = 21 - x
Now, we'll substitute this expression for y in the second equation:
5x + 2(21 - x) = 66
Time to distribute and simplify:
5x + 42 - 2x = 66
Combine like terms:
3x + 42 = 66
Subtract 42 from both sides:
3x = 24
Divide both sides by 3:
x = 8
Now that we have the value of x, we can plug it back into the first equation to find y:
8 + y = 21
Subtract 8 from both sides:
y = 13
Therefore, the first number is 8 and the second number is 13. Et voila!
To find the two numbers that satisfy the given conditions, we can set up a system of equations.
Let's assume the first number is x and the second number is y.
The problem states that the sum of the two numbers is 21, so we can write the equation:
x + y = 21 (Equation 1)
The problem also states that five times the first number is added to two times the second number, resulting in 66. We can express this as another equation:
5x + 2y = 66 (Equation 2)
We now have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously.
To solve this system, we can use the method of substitution or elimination.
Let's solve it using the substitution method:
1. Solve Equation 1 for x in terms of y:
x = 21 - y
2. Substitute this value of x into Equation 2:
5(21 - y) + 2y = 66
3. Simplify and solve for y:
105 - 5y + 2y = 66
-3y = 66 - 105
-3y = -39
y = -39 / -3
y = 13
4. Substitute the value of y back into Equation 1 to find x:
x + 13 = 21
x = 21 - 13
x = 8
So, the two numbers are 8 and 13, respectively.