(8) The algebraic expression representing the given phrase is 22x ≥ 350, where x is the number of units sold by Ms. Reed.
(9) The minimum number of shares needed to achieve the required profit is 1223, using the algebraic expression 2.25x ≥ 2750, where x is the number of shares.
(10) The number of books needed to be sold for the novelist to make a profit of $10,000 is 4350, using the algebraic expression 5000 + 1.1495x ≥ 10000, where x is the number of books sold,
(8) Weekly target for Ms. Reed is $350.
The cost of each unit she sells is $22.
We assume the number of units she sold to be x.
Thus, the total sales done by Ms. Reed is $22x.
For her to remain employed, her total sales should exceed her target, which can be shown as an algebraic expression: 22x ≥ 350.
Thus, the algebraic expression representing the given phrase is 22x ≥ 350, where x is the number of units sold by Ms. Reed.
(9) Profit on each share is $2.
The additional profit is $0.25.
Thus, the total profit on each share is $2 + $0.25 = $2.25.
The required profit by the customer is $2750.
We assume the number of shares needed to be x.
Thus, the total profit made by the customer is $2.25x.
For the customer to make the required profit, we can write the algebraic expression, 2.25x ≥ 2750.
To solve this, we divide both sides by 2.25 to get:
2.25x/2.25 ≥ 2750/2.25,
or, x ≥ 1222.22.
Thus, the minimum number of shares needed to achieve the required profit is 1223.
(10) Default contract of Book Maker publisher is $5000 and 5% royalty.
The cost of the book, for which the novelist has got the contract is $22.99.
We assume the number of books sold to be x.
The royalty share on each book given to the novelist is 5% of $22.99, or, $ 5/100 * 2299/100 = $ 11495/10000 = $1.1495.
Thus, the royalty received on x number of books = $1.1495*x = $1.1495x.
Thus, the total profit to the novelist = (5000 + 1.1495x).
Since the novelist wants to make a minimum profit of $10000, we can show it as the algebraic expression:
5000 + 1.1495x ≥ 10000.
To solve this, we go as follows:
5000 + 1.1495 ≥ 10000,
or, 1.1495x ≥ 10000 - 5000,
or, 1.1495x ≥ 5000,
or, x ≥ 5000/1.1495,
or, x ≥ 4349.717.
Approximating, we get x ≥ 4350.
Thus, 4350 books need to be sold to achieve the wanted profit.
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