Final answer:
To solve this problem, we need to set up an equation using the given information. We can then simplify and solve the equation to find the value of the unknown number.
Step-by-step explanation:
To solve this problem, we need to translate the given information into an equation. Let's call the number we're looking for 'x'. The difference between the number and 10 is 'x - 10'. So, 56 times the difference between the number and 10 can be written as '56(x - 10)'. The problem states that this expression is equal to the number plus 23, which can be written as 'x + 23'. Therefore, we have the equation 56(x - 10) = x + 23.
To solve this equation, we can start by distributing 56 to 'x' and '-10' inside the parentheses. So, we have 56x - 560 = x + 23. Next, we can simplify the equation by subtracting 'x' from both sides and adding 560 to both sides. This gives us 56x - x = 23 + 560. Simplifying further, we have 55x = 583. Finally, we can solve for 'x' by dividing both sides of the equation by 55, which gives us x = 583/55. Using long division or a calculator, we find that x is approximately 10.6. So, the number we're looking for is approximately 10.6.