Question
Here is the question : IF 23A + 12B = 164 AND 4B – 5 = 11, WHAT IS THE VALUE OF A?
Option
Here is the option for the question :
- 2
- 4
- 5
- 7
The Answer:
And, the answer for the the question is :
Explanation:
Solving the second equation will help with this one. The equation 4b – 5 = 11 requires isolating the variable b in order to solve for it. To do this, we must add 5 to either side of the equation, yielding 4b = 16. By dividing each side by 4, we may determine that b = 4. Then, substitute b into the first equation, leading to 23a + 12(4) = 163, which may be reduced to 23a + 48 = 163. Next, we subtract 48 from both sides to determine that 23a = 115, and then we divide each side by 23 to get a = 5.
When solving for the value of a variable in an equation, it’s important to use algebraic techniques to isolate the variable on one side of the equation. In the case of the equation 23a + 12b = 164 and 4b – 5 = 11, the value of a can be solved for using these techniques, and the answer is 5.
To solve for a, we need to first isolate a on one side of the equation. We can do this by subtracting 12b from both sides of the equation, which gives us:
23a = 164 – 12b
Next, we can divide both sides of the equation by 23 to isolate a. This gives us:
a = (164 – 12b) / 23
Now, we need to substitute the value of b into the equation. We are given that 4b – 5 = 11, which means that 4b = 16. Solving for b, we get b = 4.
Substituting b = 4 into the equation for a, we get:
a = (164 – 12(4)) / 23
Simplifying this expression, we get:
a = (164 – 48) / 23
a = 116 / 23
a = 5
Therefore, the value of a is 5 in the equation 23a + 12b = 164 and 4b- 5 = 11.
Algebraic techniques are fundamental to solving equations and problems in mathematics. Understanding how to isolate variables and simplify expressions is essential for solving complex problems in many fields, including engineering, physics, and computer science.
problem-solving skills and critical thinking are also important in mathematics. When solving problems, it’s important to understand the underlying concepts and to approach the problem systematically. This involves breaking down the problem into smaller parts, identifying key information, and using logical reasoning to find a solution.
the value of a in the equation 23a + 12b = 164 and 4b – 5 = 11 is 5. This can be solved for using algebraic techniques, including isolating variables and simplifying expressions. Algebraic skills, problem-solving skills, and critical thinking are all important for solving problems in mathematics and many other fields.