Question

1. a) a salesman receives a $50 bonus for each $1000 in sales made in one week. a salesman makes $12 480 in sales during a week. what will his salary be?

b) for what amount of sales will the salesman receive a salary equal to $1000?
c) is it possible for the salesman to receive a salary equal to $825? justify your answer.

1. a) the cost, y, in dollars, of sending a parcel depends on its mass, x, in grams. this cost is represented on the right.

what is the cost of sending a parcel whose mass is 260 g?
b) in what interval is the mass of a parcel that cost $12.50 to send?
c) explain, using words, how to calculate the cost of sending a parcel.
(chart: cost (y) on y - axis, mass (x) on x - axis, with grid and some markings like 250, 100, 0 on axes)

Explanation:

For Question 3 (Salesman Salary Problems)

Step1: Calculate total salary

Base salary + 50×(sales/1000)
$\text{Total Salary} = 12480 + 50\times\frac{1000}{1} = 12480 + 5000 = 17480$

Step2: Find sales for $10000 salary

Set up equation: $10000 = 12480 + 50\times\frac{x}{1000}$
Rearrange: $50\times\frac{x}{1000} = 10000 - 12480 = -2480$

Step3: Check $825 salary feasibility

Compare to base salary: $825 < 12480$

Step1: Define cost per 100g rate

From grid, 100g = $\$5$, so rate = $\frac{5}{100} = 0.05$ per g

Step2: Calculate cost for 260g

Total cost = $0.05 \times 260$
$\text{Cost} = 0.05\times260 = 13$

Step3: Find mass for $\$12.50$

Mass = $\frac{12.50}{0.05}$
$\text{Mass} = \frac{12.50}{0.05} = 250$ g. Interval: $200 < x \leq 250$ g (since cost increases at 100g/50g increments matching the grid)

Step4: Explain cost calculation method

Use per-gram rate from grid

Answer:

a) $\$17480$
b) No such sales amount exists (the result would be negative sales, which is impossible)
c) No, it is not possible. The salesman's base salary is already $\$12480$, which is higher than $\$825$, so they cannot receive a salary that low.

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For Question 4 (Parcel Cost Problems)