The sum of three times a first number and twice a scond number is 43. If the second number is subtracted from twice the first number, the result is -4. Find the number.
Mainly I can't figure out is this is two problems in one or just one.
If the two numbers are x and y, we have
3x+2y = 43
2x-y = -4
The main problem as I see it is what "Find the number" means. Which number?
Thank you. That confirms what I thought. I'm not sure what it means either. We have been working with graphing so I wonder if it means find both x and y.
That would be my guess. It probably should have read "Find the numbers."
So, did you find x and y?
This problem involves two equations with two different variables, so it is indeed two problems in one.
Let's break it down step by step.
First, let's designate the first number as variable 'x' and the second number as variable 'y'.
We are given two pieces of information:
1) "The sum of three times a first number and twice a second number is 43." This can be translated into the equation: 3x + 2y = 43.
2) "If the second number is subtracted from twice the first number, the result is -4." This can be translated into the equation: 2x - y = -4.
So we have the following system of equations:
Equation 1: 3x + 2y = 43
Equation 2: 2x - y = -4
To find the values of 'x' and 'y', we can solve this system of equations simultaneously.
One common method to solve this is substitution:
First, isolate 'y' in Equation 2:
2x - y = -4
y = 2x + 4
Now substitute this value of 'y' into Equation 1:
3x + 2(2x + 4) = 43
Simplify and solve for 'x':
3x + 4x + 8 = 43
7x = 43 - 8
7x = 35
x = 35 / 7
x = 5
Now substitute the value of 'x' back into Equation 2 to solve for 'y':
2(5) - y = -4
10 - y = -4
-y = -4 - 10
-y = -14
y = 14
So, the first number (x) is 5 and the second number (y) is 14.
Therefore, the solution to the problem is x = 5 and y = 14.