Solve the Equation: 5a + 1/3a = 5 and 9a^2 + 1/25a^2 = ?
In this article, we will solve two equations: 5a + 1/3a = 5 and 9a^2 + 1/25a^2 = ?. Let's break down each equation step by step.
Equation 1: 5a + 1/3a = 5
To solve this equation, we need to combine the like terms on the left-hand side.
Step 1: Combine like terms
5a + 1/3a = 5
To add these two terms, we need to find a common denominator, which is 3. We can rewrite the first term as:
5a = 15/3a
Now, we can add the two terms:
15/3a + 1/3a = 16/3a
So, the equation becomes:
16/3a = 5
Step 2: Solve for a
16/3a = 5
To solve for a, we can multiply both sides by 3:
16a = 15
Divide both sides by 16:
a = 15/16
Therefore, the value of a is 15/16.
Equation 2: 9a^2 + 1/25a^2 = ?
To solve this equation, we need to combine the like terms on the left-hand side.
Step 1: Combine like terms
9a^2 + 1/25a^2 = ?
To add these two terms, we need to find a common denominator, which is 25. We can rewrite the first term as:
9a^2 = 225/25a^2
Now, we can add the two terms:
225/25a^2 + 1/25a^2 = 226/25a^2
So, the equation becomes:
226/25a^2 = ?
Step 2: Simplify the expression
226/25a^2 = 9.04a^2
Therefore, the value of the expression is 9.04a^2.
In conclusion, we have solved the two equations: 5a + 1/3a = 5, which gives us a = 15/16, and 9a^2 + 1/25a^2 = 9.04a^2.
