The sum of two numbers is 87. The difference of the two numbers is 63. what are the two numbers?
X with a larger number and why be the smaller number
Write an equation that expresses the information in the Sentence “the sum of two numbers is 87”
Write an equation that expresses the information in the senates “the difference of the two numbers is 63”
well, "sum" means "add" so, x+y = 87
Now, what do you think "difference" involves?
finish it up.
To solve this problem, we can create two equations based on the information given:
Let's assume the larger number is X and the smaller number is Y.
1. "The sum of two numbers is 87":
We can write the equation as X + Y = 87.
2. "The difference of the two numbers is 63":
The equation for this sentence would be X - Y = 63.
Now, we have a system of two equations:
Equation 1: X + Y = 87
Equation 2: X - Y = 63
We can solve this system using the method of elimination or substitution:
Method 1 (Elimination):
Add both equations together to eliminate Y:
(X + Y) + (X - Y) = 87 + 63
2X = 150
X = 150/2
X = 75
Now, substitute the value of X into one of the original equations (e.g., Equation 1) and solve for Y:
75 + Y = 87
Y = 87 - 75
Y = 12
Thus, the two numbers are X = 75 and Y = 12.
Method 2 (Substitution):
Solve one of the equations (e.g., Equation 2) for X or Y and substitute it into the other equation:
X - Y = 63
X = 63 + Y
Now, substitute this value of X into the other equation (e.g., Equation 1) and solve for Y:
(63 + Y) + Y = 87
2Y + 63 = 87
2Y = 87 - 63
2Y = 24
Y = 24/2
Y = 12
Once you have Y, substitute it back into the first equation to solve for X:
X + 12 = 87
X = 87 - 12
X = 75
Thus, the two numbers are X = 75 and Y = 12.