The larger of two numbers is
7
less than
twice
the smaller number. The sum of the two numbers is
44.
Find the two numbers
X = 44 - y
x = 2y - 7
Substitute 44-y for x in the second equation and solve for y. Insert that value into the first equation to solve for x. Check by putting both values into the second equation.
To find the two numbers, let's assign variables to them.
Let's say the smaller number is x, and the larger number is y.
According to the given information:
1) "The larger of two numbers is 7 less than twice the smaller number."
This can be written as: y = 2x - 7.
2) "The sum of the two numbers is 44."
This can be written as: x + y = 44.
Now we have a system of two equations:
Equation 1: y = 2x - 7
Equation 2: x + y = 44
We can solve this system of equations using substitution or elimination method:
Let's solve using the substitution method:
Step 1: Solve equation 1 for y:
y = 2x - 7
Step 2: Substitute the value of y in equation 2:
x + (2x - 7) = 44
Step 3: Simplify and solve for x:
3x - 7 = 44
3x = 51
x = 17
Step 4: Substitute the value of x back into equation 1 to find y:
y = 2(17) - 7
y = 27
Therefore, the two numbers are x = 17 and y = 27.