Question

assignment: pages 317-318
misha manages a stationary store. she buys packs of pens from a wholesaler that sells them for $8 each. the wholesaler also charges a fee of $200 for each bulk purchase. misha then sells the packs of pens for $12 each.
1 write an equation to represent the cost to buy packs of pens from the wholesaler. then write a second equation to represent the amount of money the store will earn from selling the packs of pens. describe what your variables represent in each equation.
2 calculate the cost to buy 30 packs of pens from the wholesaler.
3 calculate the amount of money the store earns from selling 30 packs of pens.
4 calculate the profit the store will make from selling 30 packs of pens. interpret the meaning of your answer.
5 complete the table to show the cost of buying packs of pens from the wholesaler and income for different numbers of packs.

number of packs	cost from wholesaler ($)	income ($)
0
10
30
45
70
100

4 fill in the blank 1 point

1. calculate the amount of money the store earns from selling 30 packs of pens.

if the store sells 30 packs of pens, it will earn $ type your answer..
5 fill in the blank 2 points

1. calculate the profit the store will make from selling 30 packs of pens.

the cost to buy 30 packs of pens from the wholesaler is choose your answer... the income from selling 30 packs of pens, so the profit is $ type your answer...

Explanation:

Sub - question 3 (Calculate the amount of money the store earns from selling 30 packs of pens)

Step 1: Identify the selling price per pack

The store sells each pack of pens for $12. Let \( n \) be the number of packs sold. The income (earnings) from selling pens is calculated by multiplying the number of packs sold by the selling price per pack. The formula for income \( I \) is \( I = 12n \).

Step 2: Substitute the number of packs (n = 30) into the formula

We substitute \( n = 30 \) into the formula \( I=12n \). So, \( I = 12\times30 \).

Step 3: Calculate the product

\( 12\times30 = 360 \).

for cost calculation:

Step 1: Identify the cost components

The wholesaler sells each pack for $8 and charges a $200 fee for bulk purchase. Let \( n \) be the number of packs. The cost \( C \) to buy pens from the wholesaler is given by the formula \( C=8n + 200 \).

Step 2: Substitute n = 30 into the cost formula

Substitute \( n = 30 \) into \( C = 8n+200 \). So, \( C=8\times30 + 200 \).

Step 3: Calculate the cost

First, calculate \( 8\times30=240 \), then \( 240 + 200=440 \). So the cost to buy 30 packs is $440.
Now, we know from sub - question 3 that the income from selling 30 packs is $360. Wait, no, wait. Wait, there is a mistake here. Wait, no, the income from selling 30 packs is $360? Wait, no, wait, no, the selling price per pack is $12, 30 packs: 12*30 = 360? But the cost is 8*30+200=240 + 200 = 440. Then profit is income - cost. But 360-440=- 80? That can't be right. Wait, no, maybe I made a mistake in the cost formula. Wait, the problem says "the wholesaler that sells them for $8 each. The wholesaler also charges a fee of $200 for each bulk purchase". So cost LXI0. For n = 30, C=8*30 + 200=240 + 200 = 440. Income is 12*30 = 360. Then profit is 360 - 440=-80? But that would be a loss. But maybe I misread the selling price. Wait, the problem says "Misha then sells the packs of pens for $12 each". So income is 1230 = 360. Cost is 830+200 = 440. So profit is 360 - 440=-80. But let's check again.

Wait, maybe the first step of sub - question 4:

First, calculate cost:

Step 1: Cost formula

Cost \( C=8n + 200 \), n = 30. So \( C = 8\times30+200=240 + 200 = 440 \).

Step 2: Income formula (from sub - question 3)

Income \( I = 12n \), n = 30, so \( I=360 \).

Step 3: Profit formula

Profit \( P=I - C \). So \( P = 360-440=- 80 \). But this is a loss. But maybe there is a mistake in my understanding. Wait, no, the problem says "profit", but if income is less than cost, it's a loss (negative profit).

But let's check the second part of sub - question 4: "The cost to buy 30 packs of pens from the wholesaler is [less than/greater than] the income from selling 30 packs of pens, so the profit is $[answer]".

Since 440>360, the cost is greater than the income. Then profit \( P=360 - 440=-80 \).

for profit calculation:

Step 1: Recall income and cost

Income from selling 30 packs (from sub - question 3) is $360. Cost to buy 30 packs: \( C = 8\times30+200=440 \).

Step 2: Calculate profit

Profit \( P=\text{Income}-\text{Cost}=360 - 440=- 80 \).

Answer:

360

Sub - question 4 (Calculate the profit the store will make from selling 30 packs of pens)

First, we need to find the cost to buy 30 packs of pens from the wholesaler.