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 a 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
Part A:
9a + 12y = 288
Part B:
If Lauren orders only chicken dinners, she can order a maximum number of 32 dinners.
Part C:
If Lauren orders only steak dinners, she can order a maximum number of 24 dinners.
PART A
The cost of a chicken dinner is $9 per plate, so the total cost of the chicken dinners can be obtained by multiplying the number of chicken dinners by 9. Similarly, the cost of a steak dinner is $12 per plate. Thus, the total cost of the steak dinners can be obtained by multiplying the number of steak dinners by 12.
The equation that represents this situation is:
9a + 12y = 288, where a represents the number of chicken dinners and y represents the number of steak dinners.
PART B
If Lauren orders only chicken dinners, the equation becomes 9a = 288. To find the number of chicken dinners she can order, we need to solve for a.
Divide both sides of the equation by 9:
(9a)/9 = 288/9,
a = 32.
Therefore, 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 she can order, we need to solve for y.
Divide both sides of the equation by 12:
(12y)/12 = 288/12,
y = 24.
Therefore, Lauren can order 24 steak dinners.
PART A:
To complete the equation that represents this situation, we need to consider the cost of each dinner option multiplied by the number of dinners ordered.
The cost of a chicken dinner is $9 per plate, so the expression for the cost of the chicken dinners would be 9a.
Similarly, the cost of a steak dinner is $12 per plate, so the expression for the cost of the steak dinners would be 12y.
Since Lauren's budget is $288, the equation can be written as:
9a + 12y = 288
PART B:
To determine how many chicken dinners Lauren can order, we need to find the value of a.
Since only chicken dinners are being ordered, the equation simplifies to:
9a = 288
To solve for a, we divide both sides of the equation by 9:
a = 288 / 9
a = 32
Thus, Lauren can order 32 chicken dinners.
PART C:
To determine how many steak dinners Lauren can order, we need to find the value of y.
Since only steak dinners are being ordered, the equation simplifies to:
12y = 288
To solve for y, we divide both sides of the equation by 12:
y = 288 / 12
y = 24
Thus, Lauren can order 24 steak dinners.