Lauren is planning a catered dinner party for her parents' anniversary with a dinner budget of $288.
She has selected two options: a chicken dinner that costs $9 per plate and a steak dinner that costs $12 per plate. Lauren is working on the guest list and must also determine how many of each meal to order.
Let a represent the number of chicken dinners and let y represent the number of steak dinners.
Complete the equation that represents this situation.
Make sure that you write the coefficient first, then the variable. For example 3 times x should be entered 3x and 5 times y should be entered 5y.
_ = 288
PART B
• If Lauren orders only chicken dinners, how many dinners can she order?
Enter the number in the box.
_ chicken dinners
PART C
• If Lauren orders only steak dinners, how many dinners can she order?
Enter the number in the box.
_steak dinners
The equation representing this situation is:
9a + 12y = 288
PART B:
If Lauren orders only chicken dinners, the equation becomes:
9a = 288
To find the number of chicken dinners Lauren can order, we can divide both sides of the equation by 9:
a = 32
So, Lauren can order 32 chicken dinners.
PART C:
If Lauren orders only steak dinners, the equation becomes:
12y = 288
To find the number of steak dinners Lauren can order, we can divide both sides of the equation by 12:
y = 24
So, Lauren can order 24 steak dinners.
PART A:
The equation that represents this situation is:
9a + 12y = 288
PART B:
If Lauren orders only chicken dinners, the equation will be:
9a = 288
To find the number of dinners, we need to solve for 'a'. Dividing both sides of the equation by 9:
a = 288 / 9
a = 32
Therefore, Lauren can order 32 chicken dinners.
PART C:
If Lauren orders only steak dinners, the equation will be:
12y = 288
To find the number of dinners, we need to solve for 'y'. Dividing both sides of the equation by 12:
y = 288 / 12
y = 24
Therefore, Lauren can order 24 steak dinners.
In this scenario, we are given the budget of $288 for Lauren's catered dinner party. We also have the information that the chicken dinner costs $9 per plate and the steak dinner costs $12 per plate.
To determine the equation that represents this situation, we need to consider the number of chicken dinners (a) and the number of steak dinners (y) that Lauren plans to order. We know that the total cost should equal the budget of $288.
The equation can be written as:
9a + 12y = 288
Now let's move on to the next parts of the question:
PART B
If Lauren orders only chicken dinners, we need to find out how many dinners she can order. In this case, the number of steak dinners (y) would be zero. So, we substitute y with 0 in the equation:
9a + 12(0) = 288
Simplifying the equation, we have:
9a + 0 = 288
9a = 288
To solve for 'a,' we divide both sides of the equation by 9:
a = 288/9
Evaluating the expression, we find:
a = 32
Therefore, if Lauren orders only chicken dinners, she can order 32 dinners.
PART C
Similarly, if Lauren orders only steak dinners, we need to find out how many dinners she can order. In this case, the number of chicken dinners (a) would be zero. So, we substitute a with 0 in the equation:
9(0) + 12y = 288
Simplifying the equation, we have:
0 + 12y = 288
To solve for 'y,' we divide both sides of the equation by 12:
y = 288/12
Evaluating the expression, we find:
y = 24
Therefore, if Lauren orders only steak dinners, she can order 24 dinners.