Solve for a: 7a - 467.56 - (7a x 13% x 10%) + 183.36 = 260.

Step-by-step solution

1. 1

   Turn both percentages into decimals and multiply them together first. $13\%=0.13$ and $10\%=0.10$, so

   $0.13\times 0.10=0.013$

   Taking a percentage of a percentage multiplies the two decimals; the result is $1.3\%$, not $23\%$ and not $13\%$. This single line decides the whole problem.

2. 2

   Apply the combined rate to the $7a$.

   $7a\times 0.013=0.091a$

   so the equation becomes

   $7a-467.56-0.091a+183.36=260$

3. 3

   Combine the like terms on each side. Variables:

   $7a-0.091a=6.909a$

   Constants:

   $-467.56+183.36=-284.20$

   giving $6.909a-284.20=260$. Because the deduction is tiny, the coefficient stays close to $7$ and firmly positive.

4. 4

   Isolate the variable term. Add $284.20$ to both sides:

   $6.909a=544.20$

5. 5

   Divide and round sensibly.

   $a=\frac{544.20}{6.909}=78.7668\ldots\approx 78.77$

6. 6

   Check by substituting back. With $a=78.7668$: $7a=551.37$, the deduction is $0.091\times 78.7668=7.17$, and $551.37-467.56-7.17+183.36=260.00$ ✓.