What is the value of $a$ in the equation $5 a-10 b=45$, when $b=3$?
Answer (1)
Substitute b = 3 into the equation 5 a − 10 b = 45 .
Simplify the equation to 5 a − 30 = 45 .
Add 30 to both sides to get 5 a = 75 .
Divide by 5 to find a = 15 .
Explanation
Understanding the Problem We are given the equation 5 a − 10 b = 45 and the value b = 3 . Our goal is to find the value of a .
Substitution Substitute b = 3 into the equation: 5 a − 10 ( 3 ) = 45
Simplification Simplify the equation: 5 a − 30 = 45
Isolating the term with 'a' Add 30 to both sides of the equation: 5 a = 45 + 30
Further Simplification Simplify further: 5 a = 75
Solving for 'a' Divide both sides by 5 to solve for a : a = 5 75
Final Calculation Calculate the value of a : a = 15 Therefore, the value of a is 15.
Examples
Imagine you're buying apples and bananas. Each apple costs a dollars and each banana costs b dollars. You buy 5 apples and your friend buys 10 bananas. The total cost is $45. If each banana costs $3, we can use the equation 5 a − 10 b = 45 to find the cost of each apple. Substituting b = 3 , we find that each apple costs $15. This problem demonstrates how algebraic equations can be used to solve real-world problems involving costs and quantities.
