Rashid is helping to plan a cookout. He determines that making one making one hot dogs costs 55 cents and making a hamburger costs 90 cents. The cost must be no more than $50, and he knows that he must at least 60 hot dogs and hamburgers.
Which system of linear inequaltites describes the conditions in the problem?
a) 0.55x + 0.9y >= 50, x + y >= 60
b) 0.55x + 0.9y <= 50, x + y >= 60
c) 0.55x + 0.9y >= 50, x + y <= 60
d) 0.55x + 0.9y <= 50, x + y <= 60
and the answer i picked was c
thank you !!!!!!!!!!!!!!!!!!!!
Since it needs to be "at least 60" x + y ≥ 60.
"no more than $50" = less than or equal to = 0.55x + 0.9y ≤ 50
To determine the correct system of linear inequalities that describes the conditions in the problem, we need to carefully analyze the given information.
Let's break down the problem step by step:
1. Rashid wants to make hot dogs and hamburgers for the cookout.
2. The cost of making one hot dog is $0.55, and the cost of making one hamburger is $0.90.
3. The maximum budget for the cookout is $50.
4. Rashid must make at least 60 hot dogs and hamburgers combined.
We can define two variables to represent the number of hot dogs (x) and hamburgers (y) that Rashid makes for the cookout.
Now let's address the conditions mentioned in the problem with inequalities:
1. Cost Constraint: The cost of making hot dogs and hamburgers must be no more than $50.
The cost of x hot dogs is 0.55x, and the cost of y hamburgers is 0.9y.
Therefore, the inequality representing the cost constraint is 0.55x + 0.9y <= 50.
2. Quantity Constraint: Rashid must make at least 60 hot dogs and hamburgers combined.
To represent this constraint, we need to define a total quantity variable.
The number of hot dogs (x) plus the number of hamburgers (y) must be greater than or equal to 60.
Therefore, the inequality representing the quantity constraint is x + y >= 60.
Now that we have defined the inequalities representing the cost and quantity constraints, let's compare the options provided:
a) 0.55x + 0.9y >= 50, x + y >= 60
b) 0.55x + 0.9y <= 50, x + y >= 60
c) 0.55x + 0.9y >= 50, x + y <= 60
d) 0.55x + 0.9y <= 50, x + y <= 60
By comparing the inequalities we derived with the answer choices, we can see that the correct answer is option d) 0.55x + 0.9y <= 50, x + y <= 60.
This option is the correct choice because it satisfies both the cost constraint (less than or equal to $50) and the quantity constraint (less than or equal to 60 hot dogs and hamburgers).
It is worth noting that option c) does not represent the quantity constraint correctly since it states x + y <= 60, which contradicts Rashid's requirement of making at least 60 hot dogs and hamburgers combined.
I hope this explanation helps clarify the reasoning behind selecting option d) as the correct answer.