11. The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. Find the numbers by writing and solving a system of equations.
Let's call the first number "x" and the second number "y".
From the first sentence, we know that:
y = 2x + 5
From the second sentence, we know that:
x + y = 44
Now we have two equations with two variables, which we can solve for x and y.
We can start by substituting the first equation into the second equation:
x + (2x + 5) = 44
Simplifying, we get:
3x + 5 = 44
Subtracting 5 from both sides:
3x = 39
Dividing both sides by 3:
x = 13
Now that we know x is 13, we can use the first equation to find y:
y = 2x + 5
y = 2(13) + 5
y = 31
So the two numbers are 13 and 31.
Let's assume the first number is x and the second number is y.
According to the given information:
1. The second number is 5 more than twice the first. This can be written as y = 2x + 5.
2. The sum of the numbers is 44. This can be written as x + y = 44.
We now have a system of equations:
y = 2x + 5 (equation 1)
x + y = 44 (equation 2)
To solve this system, we can use the substitution method.
We'll start by solving equation 1 for y:
y = 2x + 5
Now substitute this value of y into equation 2:
x + (2x + 5) = 44
Simplify the equation:
3x + 5 = 44
Subtract 5 from both sides of the equation:
3x = 39
Divide both sides of the equation by 3:
x = 13
Now substitute this value of x back into equation 1 to find y:
y = 2(13) + 5
y = 26 + 5
y = 31
Therefore, the first number is 13 and the second number is 31.
To solve this problem, we can set up a system of equations based on the given information.
Let's start by assigning variables to the unknown numbers. Let's say the first number is x and the second number is y.
According to the problem, the second number is 5 more than twice the first. So we can express this relationship as:
y = 2x + 5 (Equation 1)
The sum of the numbers is 44. So we can write another equation:
x + y = 44 (Equation 2)
Now we have a system of equations consisting of Equations 1 and 2. We can solve this system using substitution or elimination method.
Let's solve it using substitution:
Step 1: Solve Equation 1 for y.
y = 2x + 5
Step 2: Substitute the value of y from Equation 1 into Equation 2.
x + (2x + 5) = 44
Step 3: Simplify and solve for x.
3x + 5 = 44
3x = 44 - 5
3x = 39
x = 39 / 3
x = 13
Step 4: Substitute x = 13 into Equation 1 to find y.
y = 2(13) + 5
y = 26 + 5
y = 31
Therefore, the first number is 13 and the second number is 31.