Final answer:
To determine the value of a when the sum of two numbers is 8.25 and the difference is 0.75, we can set up the equation 2a = 9.
Step-by-step explanation:
The sum of two numbers, a and b, is 8.25. The difference between the two numbers is 0.75. To determine the value of a, we can set up the equation:
a + b = 8.25
Since the difference between the two numbers is 0.75, we can also set up the equation:
a - b = 0.75
To solve these equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From the first equation, we can solve for b:
b = 8.25 - a
Now, substitute this value of b into the second equation:
a - (8.25 - a) = 0.75
Simplify the equation:
2a - 8.25 = 0.75
Add 8.25 to both sides:
2a = 9
Divide both sides by 2:
a = 4.5
So, the correct equation to determine the value of a is: 2a = 9.