Question

Sharon earns $25 per item she sells plus a base salary of $100 per week. Write and solve an inequality to find how many items she must sell to earn at least $700 per week. Provide your conclusion as a complete sentence.

Answer 1

The amount she earns is based on two parts.
Can you name what the two parts are?

Answer 2

"Sharon earns $25 per item she sells plus a base salary of $100 per week."

Answer 3

25 dollars per item she sells.. And 100 dollars as a base pay of salary

Answer 4

Correct.
The amount she earns in a week comes from those two parts.
She earns $100 base salary. This is a fixed part of her salary. No matter how much she sells, she will earn $100.
Then she earns an additional $25 for each item she sells. If she sells no items in 1 week, this part will give her $0. If she sells 1 item in 1 week, she will earn $25 from this part. Etc.

Answer 5

weekly salary = fixed part + part per item

The fixed part is $100, so we replace "fixed part" with 100

weekly salary = 100 + part per item

Answer 6

Let's let x represent the number of items she sells in a week.
Since she earns $25 for each item, how much will she earn from selling x number of items?

Answer 7

600? Since 100 of that is salary

Answer 8

No. Let me try to explain that better.
We are not dealing with the fixed part of the salary, the $100, for now.
We are just dealing with the amount she earns per each item she sells.
For 1 item she earns $25.
For selling 2 items she earns 2 * $25 = $50
For selling x items, how much does she earn?

Answer 9

Since she earns $25 per item she sells, if you multiply the number of items by $25, you get how much she earned from the number of items she sold. The part of the salary the depends on the number of items sold is calculated by multiplying the number of items sold by $25.
If she sells 1 item, she earns 1 * $25 = $25
If she sells 2 items, she earns 2 * $25 = $50
If she sells 3 items, she earns 3 * $25 = $75
If she sells x items, how much will she earn?

Answer 10

If she sells 24 things she'll make 600 dollars

24*25=600

600/25=24

Answer 11

Yes, and if she sells x items?

Answer 12

I'm sorry but I'm confused?

Answer 13

If she sells x items, she will make 25x on the number of items.
The total amount she earns from the base salary and the items she sells is

total weekly salary = fixed part + part per item

total weekly salary = 100 + 25x

for selling x items

Answer 14

100+25(24)=700
Is this right?

Answer 15

I see that you understand that 24 items at $25 each means 24 * $25 = $600.
The problem is that we don't know what the answer of the problem is.
We are dealing with an unknown number of items represented by the variable x.
We need an expression of how much she earns for selling x items at $25 each.
The expression is 25x. Just like if she sells 24 items she earns 24 * 25, then if she sells x items, she earns x * 25 which is written as 25x.

Answer 16

Her weekly salary is

100 + 25x

She wants this salary to be at least $700, so we write an inequality:

\(100 + 25x \ge 700\)

Answer 17

Now we have an inequality that states that the amount she earns from the base salary plus what she earns from the sales of the items must be at least (greater than or equal to) $700.

Answer 18

Now you need to solve the inequality.

Answer 19

\(100 + 25x \ge 700\)

Subtract 100 from both sides:

\(25x \ge 600\)

Divide both sides by 25:

\(x \ge 24\)

The answer is: she must at least 24 items in a week to earn at least than $700 in that week.

Answer 20

100+25x > 700
-100 -100
25x > 600
Divide both sides by 25
x is greater than or equal to 24

Okay thanks.. I just really suck at this whole Algebra thing ):

Answer 21

Everything above is correct, but you must use \(\ge\), not just >.
She wants to earn at least 700, that means she can earn just $700, not just more than $700.

Answer 22

On a computer, you can use >= to mean "greater than or equal to."

Answer 23

Okay thank you so much!