When faced with the equation A+B+B+B+80+90=100A + B + B + B + 80 + 90 = 100A+B+B+B+80+90=100, it can be a bit perplexing if you’re not sure how to approach it. But don’t worry! In this blog, we’ll break down the process of solving this equation logically and clearly.
We are sharing the complete details of the Math Equation A+B+B+B+80+90=100 with you. This will be very helpful for you, and if you have any confusion or get stuck somewhere, you can avail our Linear Algebra services, which will be very beneficial for you.
Understanding the Equation
The given equation is:
A+B+B+B+80+90=100A + B + B + B + 80 + 90 = 100A+B+B+B+80+90=100
Let’s simplify and solve it step-by-step.
Step 1: Simplify the Equation
First, combine the terms involving BBB on the left side of the equation. Notice that BBB appears three times, so you can simplify this to:
A+3B+80+90=100A + 3B + 80 + 90 = 100A+3B+80+90=100
Now, add the constants 808080 and 909090:
A+3B+170=100A + 3B + 170 = 100A+3B+170=100
Step 2: Isolate the Variables
Next, isolate the variables by subtracting 170 from both sides of the equation:
A+3B+170−170=100−170A + 3B + 170 – 170 = 100 – 170A+3B+170−170=100−170
This simplifies to:
A+3B=−70A + 3B = -70A+3B=−70
Step 3: Analyze the Solution
At this point, you have:
A+3B=−70A + 3B = -70A+3B=−70
To solve for AAA and BBB, you need additional information or constraints. Without extra information, AAA and BBB can be any pair of numbers that satisfy this equation.
Step 4: Find Possible Solutions
Let’s explore a few solutions to illustrate how AAA and BBB might work. You can choose a value for BBB and solve for AAA, or vice versa.
Example 1:
- Let B=0B = 0B=0:
A+3(0)=−70A + 3(0) = -70A+3(0)=−70
A=−70A = -70A=−70
So one solution is A=−70A = -70A=−70 and B=0B = 0B=0.
Example 2:
- Let B=−10B = -10B=−10:
A+3(−10)=−70A + 3(-10) = -70A+3(−10)=−70
A−30=−70A – 30 = -70A−30=−70
A=−40A = -40A=−40
Another solution is A=−40A = -40A=−40 and B=−10B = -10B=−10.
Step 5: General Solution
In general, the equation A+3B=−70A + 3B = -70A+3B=−70 can be solved for AAA in terms of BBB:
A=−70−3BA = -70 – 3BA=−70−3B
So, for any value of BBB, you can find a corresponding AAA.
Read more: How to Solve a Variable Equation
Conclusion
To solve the equation A+B+B+B+80+90=100A + B + B + B + 80 + 90 = 100 logically, you first simplify the terms and then isolate the variables. Once you have the simplified equation A+3B=−70A + 3B = -70, you can find multiple solutions depending on the values you choose for BB. This process demonstrates how to approach equations with multiple variables and shows that there can be multiple valid solutions depending on the constraints given. For more detailed guidance on solving math problems, visit Allassignmenthelp.org.
Frequently Asked Questions
How do you simplify the equation A + B + B + B + 80 + 90 = 100?
First, combine the like terms. B + B + B = 3B. Then add the constants 80 + 90 = 170. The equation becomes A + 3B + 170 = 100.
Why doesn’t this equation have a single answer?
Because there are two variables (A and B) but only one equation. With more variables than equations, you get infinite possible solutions, not just one.
What is the general solution of the equation?
After simplification, the equation is A + 3B = –70. Rearranging gives A = –70 – 3B. This shows that for any chosen value of B, you can find a matching value of A.
Can you solve for A when B = 0?
Yes. If B = 0, the equation becomes A + 3(0) = –70, so A = –70. That means one valid solution is A = –70 and B = 0.
How can students check if their solution is correct?
Simply substitute the values of A and B back into the original equation A + B + B + B + 80 + 90 = 100. If both sides equal 100, the solution is correct.
