SOLVE a smaller number and a larger number add up to 9 and have a difference of 5. Let x be the larger number and y be the smaller number.
Letx+y=9 and x-y=5
then 2x=14
x=7
then y=2
Let's solve this problem step-by-step:
Step 1: Write down the given information:
The sum of a smaller number and a larger number is 9.
The difference between the larger number and the smaller number is 5.
Step 2: Translate the given information into equations:
x + y = 9 (Equation 1, where x is the larger number and y is the smaller number)
x - y = 5 (Equation 2)
Step 3: Solve the system of equations (Equation 1 and Equation 2):
To solve the system of equations, we can use the method of elimination. We can add Equation 1 and Equation 2 together to eliminate the variable y:
(x + y) + (x - y) = 9 + 5
2x = 14
x = 7
Step 4: Substitute the value of x back into one of the original equations to solve for y:
Using Equation 1:
7 + y = 9
y = 2
Step 5: Check the solution:
Let's check whether the values of x = 7 and y = 2 satisfy both equations:
Equation 1: 7 + 2 = 9 (satisfied)
Equation 2: 7 - 2 = 5 (satisfied)
Therefore, the larger number (x) is 7 and the smaller number (y) is 2.
To solve this problem, we will set up a system of equations using the given information.
Let x be the larger number and y be the smaller number.
From the problem, we know that the two numbers add up to 9:
x + y = 9 (equation 1)
We also know that the larger number is 5 more than the smaller number:
x = y + 5 (equation 2)
To solve this system of equations, we can use the method of substitution.
Substitute the value of x from equation 2 into equation 1:
(y + 5) + y = 9
Simplify the equation:
2y + 5 = 9
Subtract 5 from both sides:
2y = 4
Divide both sides by 2:
y = 2
Now that we have the value of y, we can substitute it back into either equation 1 or 2 to find the value of x.
Substituting y = 2 into equation 1:
x + 2 = 9
Subtract 2 from both sides:
x = 7
So, the smaller number (y) is 2 and the larger number (x) is 7.