Solve 0.85x + 0.85x = 87870 for x.

Step-by-step solution

1. 1

   Add the two identical terms. They are like terms, so the coefficients add:

   $0.85x+0.85x=2(0.85x)=1.70x$

   The standard slip is to leave $0.85x$ on the left, which doubles the final answer.

2. 2

   Divide by the combined coefficient.

   $x=\frac{87870}{1.70}$

3. 3

   Clear the decimal to get an exact fraction. Multiply numerator and denominator by $100$, then cancel the common factor $10$:

   $\frac{87870}{1.7}=\frac{8787000}{170}=\frac{878700}{17}$

   Since $17$ is prime and does not divide $878700$, this fraction is already in lowest terms — the answer cannot be a whole number.

4. 4

   Carry out the division. $17\cdot 51688=878696$, leaving a remainder of $4$, so

   $x=51688+\frac{4}{17}=51688.23529411\ldots$

   The repeating block comes from $4/17$; rounding to cents gives $x\approx 51688.24$.

5. 5

   Check. $1.7\times 51688.2352941=87870.0000$, and equivalently $0.85\times 51688.2352941=43935$, which doubled is $87870$. Both routes reproduce the right-hand side.