1)

Let's assume that Reza was losing x pounds per week and James was losing y pounds per week. Then, after 10 weeks, Reza would weigh 185 - 10x pounds and James would weigh 18 - 10y pounds.

If after 10 weeks Reza weighed less than James, the inequality to...

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1)

Let's assume that Reza was losing x pounds per week and James was losing y pounds per week. Then, after 10 weeks, Reza would weigh 185 - 10x pounds and James would weigh 18 - 10y pounds.

If after 10 weeks Reza weighed less than James, the inequality to describe the situation would be

185 - 10x < 180 - 10y

To determine the constraints on the variables x and y, combine the variable terms on the right side and the numbers on the left side:

185 - 180 < 10x - 10y

5 < 10(x - y)

Dividing both sides by 0 yields

x - y > 0.5 or x > y + 0.5

This means, that in order for Reza to weigh less than James after 10 weeks, her weight loss per week has to be by half a pound greater than James's weight loss per week.

2) Denote the number of pies Nell is going to sell by p. Then, she is going to make $10p by selling p pies, since she charges $10 per pie. Since she spends $65 on materials, her net profit will be, in dollars, 10p - 65.

If Nell is going to spend t hours at the market, and wants to make at least $15 per hour, then she wants her net profit to be at least $15t.

The inequality that describes the situation is

`10p - 65 >=15t`

From here,

`10p - 15t >=65`

Dividing both sides by 5 yields

`2p - 3t >=13`

Nell could use the above inequality to set constraints on the number of pies she should make. For example, if she wants to spend t = 3 hours at the market, she would have to make and sell at least p pies, where p is

`2p - 3*3 >=13`

` ` `2p>=22`

`p>=11`

If Nell wants to spend 3 hours at the market, she would have to make and sell at least 11 pies, in order to have profit of at least $15 an hour.

Alternatively, if Nell could set constraints on the time spent at the market. If, for example, she had make p = 16 pies, the time she should spend at the market is determined by

`2*16- 3t >=13`

`3t<=32-13 `

`3t<=9`

`t<=3`

Nell would have to spend no more than 3 hours at the market selling 16 pies, if she wants to make at least $15 per hour.