Solve and check the following equation.
\[
0.11 y+0.08(y+8000)=1970
\]
Final Answer: The solution to the equation is \(\boxed{7000}\).
Step 1 :Simplify the given equation 0.11y + 0.08(y + 8000) = 1970.
Step 2 :Combine like terms to get 0.19y + 640 = 1970.
Step 3 :Subtract 640 from both sides to isolate the term with y, resulting in 0.19y = 1330.
Step 4 :Divide both sides by 0.19 to solve for y, yielding y = 7000.
Step 5 :Check the solution by substituting y = 7000 back into the original equation.
Step 6 :0.11(7000) + 0.08(7000 + 8000) = 1970, which simplifies to 1970 = 1970, confirming that the solution is correct.
Step 7 :Final Answer: The solution to the equation is \(\boxed{7000}\).