Question

1. 200 less than half of a number
2. 3 times the difference of a number squared and 82
3. 999 less than 45 increased by the product of a number and 65

Explanation:

Step1: Define variable for number

Let the unknown number be $x$.

Step2: Translate problem 4 to expression

Half the number minus 200: $\frac{1}{2}x - 200$

Step3: Translate problem 5 to expression

3 times (number squared minus 82): $3(x^2 - 82)$

Step4: Translate problem 6 to expression

45 plus product minus 999: $(45 + 65x) - 999$

Step5: Simplify problem 6 expression

Combine constant terms: $65x - 954$

Answer:

1. $\frac{1}{2}x - 200$
2. $3(x^2 - 82)$
3. $65x - 954$