Question

FOR # 13-#14: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100.

13. Write the inequality and solve the inequality for the number of sales you need to make.
14. Graph your inequality from #13 on a number line.
15. For n(34-n) <111, check whether n = -3 is a solution.
SOLUTION? (Yes or No)______

Answer 1

13. x ≥ 50/3

14. attached graph

15. Yes

Explanation:

Answer 2

13) x ≥ 50/3

14) see attached graph

15) Yes

Explanation:

The equation relating the number of sales and pay is given by

y = 50 + 3x where x is the number of sales.

Q 13

If you need your pay to be exactly 100 then the above equation translates to 50 + 3x = 100

If you want the sales to be at least 100 then the above equation becomes an inequality 50 + 3x ≥ 100
We can re-write this as x ≥ 50/3

Q 14

See attached graph

x = 50/3 is a vertical line passing intersecting the x axis at x = 50/3(16.67)

All values of x ≥ 16.67 forms the region for the inequality

Q 15

Substitute -3 for n in the equation n(34-n) and check whether it satisfies the inequality

(-3)(34 - (-3)) = (-3)(37) is a negative number. (You don't actually have to calculate it but it works out to -111. ) Therefore it satisfies the inequality
n(n-34) < 111 Answer: YES