Which is the solution to the equation $2.6 a +18.4=28.8$? Round to the nearest tenth if necessary.
A. 1.4
B. 4
C. 182
D. 27
Answer (2)
Subtract 18.4 from both sides: 2.6 a = 28.8 − 18.4 .
Calculate the difference: 2.6 a = 10.4 .
Divide both sides by 2.6: a = 2.6 10.4 .
Calculate the value of a : a = 4 . The solution is 4 .
Explanation
Understanding the Problem We are given the equation 2.6 a + 18.4 = 28.8 and asked to find the value of a , rounding to the nearest tenth if necessary.
Isolating the Term with 'a' First, we need to isolate the term with a on one side of the equation. To do this, we subtract 18.4 from both sides of the equation: 2.6 a + 18.4 − 18.4 = 28.8 − 18.4 2.6 a = 28.8 − 18.4
Calculating the Difference Now, we calculate the difference: 28.8 − 18.4 = 10.4 . So, we have: 2.6 a = 10.4
Solving for 'a' Next, we need to solve for a by dividing both sides of the equation by 2.6: a = 2.6 10.4
Calculating the Value of 'a' Now, we perform the division: a = 2.6 10.4 = 4 .
Final Answer Since a = 4 , it is already an integer. Therefore, no rounding is necessary. The solution is a = 4 .
Examples
Imagine you're buying apples at a store. Each apple costs $2.6, and you also have a fixed cost of $18.4 for a basket. If your total bill is $28.8, this problem helps you calculate how many apples you bought. Solving linear equations like this is useful in many everyday situations, such as budgeting, calculating costs, and determining quantities.
The solution to the equation 2.6 a + 18.4 = 28.8 is a = 4 . This was determined by isolating a and solving the equation. The selected answer is option B, 4.
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