Which equation is equivalent to $-k+0.03+1.01 k=-2.45-1.81 k$?

A. $-100 k+3+101 k=-245-181 k$
B. $-100 k+300+101 k=-245-181 k$
C. $-k+3+101 k=-245-181 k$
D. $-k+300+101 k=-245-181 k$

The equivalent equation to − k + 0.03 + 1.01 k = − 2.45 − 1.81 k is − 100 k + 3 + 101 k = − 245 − 181 k , which corresponds to option A.
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Answered by Anonymous | 2025-07-07

Multiply the original equation by 100 to eliminate decimals.
Simplify the equation: − 100 k + 3 + 101 k = − 245 − 181 k .
Compare the simplified equation with the given options.
The equivalent equation is: − 100 k + 3 + 101 k = − 245 − 181 k ​ .

Explanation

Problem Analysis We are given the equation − k + 0.03 + 1.01 k = − 2.45 − 1.81 k and asked to find an equivalent equation from the list.

The options are:

− 100 k + 3 + 101 k = − 245 − 181 k
− 100 k + 300 + 101 k = − 245 − 181 k
− k + 3 + 101 k = − 245 − 181 k
− k + 300 + 101 k = − 245 − 181 k


Strategy To find the equivalent equation, we can multiply both sides of the original equation by 100 to eliminate the decimals. This will make it easier to compare with the given options.

The original equation is: − k + 0.03 + 1.01 k = − 2.45 − 1.81 k

Calculations Multiplying both sides of the equation by 100, we get: 100 ( − k + 0.03 + 1.01 k ) = 100 ( − 2.45 − 1.81 k ) Distribute the 100 on both sides: 100 ( − k ) + 100 ( 0.03 ) + 100 ( 1.01 k ) = 100 ( − 2.45 ) + 100 ( − 1.81 k ) Simplify: − 100 k + 3 + 101 k = − 245 − 181 k

Finding the Equivalent Equation Now, we compare the simplified equation with the given options:



− 100 k + 3 + 101 k = − 245 − 181 k This matches our simplified equation.
− 100 k + 300 + 101 k = − 245 − 181 k This does not match.
− k + 3 + 101 k = − 245 − 181 k This does not match.
− k + 300 + 101 k = − 245 − 181 k This does not match.

Therefore, the equivalent equation is − 100 k + 3 + 101 k = − 245 − 181 k .

Final Answer The equation equivalent to − k + 0.03 + 1.01 k = − 2.45 − 1.81 k is − 100 k + 3 + 101 k = − 245 − 181 k ​ .

Examples
When dealing with financial calculations involving percentages or small decimal values, converting the equation to whole numbers by multiplying by 100 can simplify the process and reduce the chance of errors. For example, if you are calculating the total cost of an item with a sales tax and a discount, converting all values to cents can make the calculations easier to manage. This approach is also useful in programming when dealing with monetary values, as it avoids floating-point precision issues.

Answered by GinnyAnswer | 2025-07-07