Translate problem situation to a system of equations. Do not solve. The sum of two numbers is 10 the first number is 2/3 of the second number. What are the numbers?
would it be 6, and 4? or 7, and 3? I know 2/3 of 10 is 6.66666667, so being after the decimal is higher than 5 usually goes up a number. Am I right?
x+y = 10
x = 2/3 y
Surely you know that 4 is 2/3 of 6
3 is clearly not 2/3 of 7
What do you care about 2/3 of 10? That was not part of the problem. The key to word problems is taking the given facts and expressing them in math symbols. It appears that you did not do that, but just started guessing.
To translate the problem situation into a system of equations, let's start by identifying the unknowns. In this case, we need to find the two numbers. Let's call the first number "x" and the second number "y".
Based on the problem statement, we can create two equations:
1. "The sum of two numbers is 10": x + y = 10
2. "The first number is 2/3 of the second number": x = (2/3)y
Now, we have a system of equations:
Equation 1: x + y = 10
Equation 2: x = (2/3)y
By solving this system, we can find the values for x and y.
Regarding your suggested answers, you estimated that the first number is 6 and the second number is 4, or vice versa. Let's check if these values satisfy the system of equations:
For x = 6 and y = 4:
Equation 1: 6 + 4 = 10 ✔️
Equation 2: 6 = (2/3)4 ❌ (Incorrect)
Therefore, the numbers 6 and 4 do not fulfill both equations.
For x = 7 and y = 3:
Equation 1: 7 + 3 = 10 ✔️
Equation 2: 7 = (2/3)3 ✔️
Hence, the numbers 7 and 3 are the correct solution to the problem.