Question

A toy company spends $20 for every doll it makes. Promotion of the dolls costs $400 and the company sells each doll for $30. How many dolls must the company sell to make a profit?

What inequality represents this problem?

Answer 1

Since the company spends 20$ on each doll and sells each for 30$ thats a 10$ profit.

If the company spends 400$ on promotion it would take 40 dolls since

400$ / 10$(amount of profit per doll) = 40

so to make the promotion back it would be 40 dolls but the question was to make PROFIT so it must be 41 dolls

Answer 2

Inequality represents this problem is
`20x+400 < 30x` and the company must sell more than 40 dolls to make a profit.

Explanation:

Cost of making 1 doll = $20

Let the no. of dolls be x

Cost of making x doll = $20x

Promotion of the dolls costs $400

So, Total cost price = 20x+400

The company sells each doll for $30

Selling price of x dolls = 30x

SP = 30x

CP =20x+400

For profit SP > CP

So, Equation :
`20x+400 < 30x`

`400 < 10x`

`40 < x`

So, the company must sell more than 40 dolls to make a profit.

Hence inequality represents this problem is
`20x+400 < 30x` and the company must sell more than 40 dolls to make a profit.