Question

Matthew wants to sell laptops and smartphones. He wants to sell at least 12 devices and earn at least $4500.

L+S≥ 12 represents the number of laptops, L and smartphones, S Matthew should sell to achieve his goal of selling at least 12 devices.

425L+125S≥4500 represents the number of laptops and smartphones he can sell to earn at least $4500.

Does Matthew meet both of his goals by selling 9 laptops and 6 smartphones?

Answer Choices:

A. Matthew meets both of his goals.

B. Matthew sells the expected number of devices but doesn't earn the expected amount of money.

C. Matthew earns the expected amount of money but doesn't sell the expected number of devices.

D. Matthew doesn't meet either of his goals.

Answer 1

He sells 15 items so he meets the goal L + S >= 12

Checking the other inequality
425*9 + 125*6 = $4575 so he achieves the second goal as well.

Answer is A.

Answer 2

A. Matthew meets both of his goals.

Explanation:

Let laptops be represented by L

Let smartphones be represented by S

Matthew wants to sell at least 12 devices and earn at least $4500.

The equation first becomes:
`L+S\geq 12`

He wants to earn $4500 by selling both products.

`425L+125S \geq 4500`

Now we have been given, that Matthew sells 9 laptops and 6 smartphones.

Lets check this:

Putting L = 9 and S = 6;

`9+6\geq 12`

=>
`15\geq 12` (condition fulfilled)

`425(9)+125(6) \geq 4500`

=>
`3825+750\geq 4500`

=>
`4575\geq 4500` (condition fulfilled)

Therefore, option A is correct- Matthew meets both of his goals.