the sum of two numbers is 18. The difference between three times the lesser number and the greater number is 10.
A)define variables and formulate a system of equations from this situation
B)solve your system of equations algebraically and find the greater number
lESSOR+LARGER=18
3*LESSOR-lARGER=10
ADD THE TWO EQUATIONS
4*LESSOR=28
LESSOR=7
lARGER=11
A) To define variables and formulate a system of equations, let's assign the variables as follows:
Let x be the lesser number.
Let y be the greater number.
From the given information, we can extract two equations:
1) The sum of two numbers is 18, which can be written as:
x + y = 18
2) The difference between three times the lesser number and the greater number is 10, which can be written as:
3x - y = 10
Therefore, our system of equations is:
Equation 1: x + y = 18
Equation 2: 3x - y = 10
B) Now, let's solve the system of equations algebraically to find the greater number.
From Equation 1 (x + y = 18), we can rewrite it as y = 18 - x.
Substitute this expression for y in Equation 2 (3x - y = 10):
3x - (18 - x) = 10
3x - 18 + x = 10
4x - 18 = 10
4x = 28
x = 7
Now, substitute the value of x back into Equation 1 to find the value of y:
7 + y = 18
y = 18 - 7
y = 11
Therefore, the greater number is 11.