Darpana solved the equation s = a+b+c/3 for a. her steps are shown below:
1. multiply by 3: s=a+b+c/3
3s=a+b+c

2. subtract b: 3s-b=a+b+c-b
3s-b=a+c
3. divide by c: 3s-b/c=a
which statement about darpana’s work is true?
in step 1 she needed to divide by 3 rather than multiply.
in step 2 she needed to add b rather than subtract.
in step 3 she needed to subtract c rather than divide.
darpana solved the equation correctly.

The true statement is: In step 3 she needed to subtract c rather than divide.

Step-by-step explanation:

Lets solve our equation step by step.

Step 1. Since 3 is the denominator of the right hand side, we need to multiply both sides of the equation by 3:

Now we can cancel the 3 in the numerator and the 3 in the denominator to get

As you can see, the first statement is false

Step 2. Since we want to isolate the variable , we need to subtract b from both sides of the equation:

The second statement is also false

Step 3. The last thing we to do to isolate (and solve for it) is subtract c from both sides of the equation:

Therefore, the third statement is true: In step 3 she needed to subtract c rather than divide.

Third option (In step 3 she needed to subtract c rather than divide)

Step-by-step explanation:

When she subtract b from both sides of the equation, she obtained:

Therefore, to leave the a alone at one member of the equation, she needs to subtract c from both sides of the equation.

Then, she would obtain the following:

Therefore the answer is the third option: In step 3 she needed to subtract c rather than divide.

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