Final answer:
To translate the problem into an algebraic expression, assign a variable to the unknown number and then solve for it by simplifying the expression.
Step-by-step explanation:
To translate the given problem into an algebraic expression, we can assign a variable to the unknown number. Let's say the number is x.
The expression "A number increased by a % and decreased by 80%" can be represented as:
x + (x * a%) - (x * 80%) = 400
Now we can solve for x by simplifying the expression and applying the correct operations.
For example, let's say the percentage increase is 10%. Then the algebraic expression would be:
x + (x * 0.10) - (x * 0.80) = 400
Simplifying further, we get:
1.1x - 0.8x = 400
0.3x = 400
x = 400/0.3