Using inequalities, the client can consume up to 6 servings of Chicken patty or up to 9 servings of Turkey while remaining under a 680 calorie limit for lunch, after already having consumed 125 calories.
To determine the number of servings of a selected protein the client can eat, we can construct an inequality. Let's choose Chicken patty as our protein. As the question states, the client has already consumed 125 calories and has a limit of 680 calories for lunch. Therefore, we have:
125 + 80x ≤ 680
Subtracting 125 from both sides gives:
80x ≤ 555
Dividing both sides by 80 we get:
x ≤ 6.9375
Since the client can't eat a fraction of a serving, we round down to the nearest whole number:
x ≤ 6
For a different protein, such as Turkey, the inequality would be:
125 + 60x ≤ 680
After simplifying, we find that:
x ≤ 9.25
And therefore:
x ≤ 9
The client can have up to 6 servings of Chicken patty or 9 servings of Turkey, staying within her calorie limit.