Solve for b. Simplify your answer as much as possible. 40 = 25b
The Correct Answer and Explanation is:
To solve the equation 40=25b40 = 25b40=25b for bbb, we need to isolate bbb on one side of the equation.
Step 1: Divide both sides by 25
We have 40=25b40 = 25b40=25b. To isolate bbb, divide both sides of the equation by 25:4025=25b25\frac{40}{25} = \frac{25b}{25}2540=2525b
This simplifies to:4025=b\frac{40}{25} = b2540=b
Step 2: Simplify the fraction
Now, simplify 4025\frac{40}{25}2540. Both 40 and 25 have a common factor of 5. Divide both the numerator and denominator by 5:40÷525÷5=85\frac{40 \div 5}{25 \div 5} = \frac{8}{5}25÷540÷5=58
Thus, b=85b = \frac{8}{5}b=58.
Final Answer:
The solution to the equation is:b=85b = \frac{8}{5}b=58
Explanation:
This is a basic algebraic equation. The goal is to isolate the variable bbb by performing the same operation on both sides of the equation. Dividing both sides by 25 is the key step to get bbb by itself. After simplifying the fraction, we get the final answer b=85b = \frac{8}{5}b=58.
This solution tells us that bbb is equivalent to 1.6, as 85\frac{8}{5}58 is a decimal number, but keeping the fraction form is often preferred in algebra for exactness.
