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 x
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
If Lauren orders only steak dinners, how many dinners can she order?
If Lauren orders only steak dinners, the equation representing this situation would be: 12y = 288.
To find out how many steak dinners she can order, we need to solve for y:
12y = 288
y = 288/12
y = 24
Lauren can order a maximum of 24 steak dinners.
If Lauren only orders steak dinners, the equation representing this situation would be:
12y = 288
To find out how many dinners she can order, we need to solve for y.
Dividing both sides of the equation by 12:
y = 288 / 12
Simplifying:
y = 24
Therefore, Lauren can order 24 steak dinners if she chooses to only order steak.
To find the equation that represents this situation, we need to consider the cost of the dinners.
The chicken dinner costs $9 per plate, so the cost of x chicken dinners will be 9x.
The steak dinner costs $12 per plate, so the cost of y steak dinners will be 12y.
Since Lauren's budget is $288, the equation representing the cost of the dinners can be written as:
9x + 12y = 288
Now, let's move on to the second question. If Lauren orders only steak dinners, we need to find out how many dinners she can order within her budget.
Using the equation 9x + 12y = 288, we can assume that Lauren orders only steak dinners, which means x = 0. Substituting this value into the equation, we get:
9(0) + 12y = 288
0 + 12y = 288
12y = 288
To find the value of y, we can divide both sides of the equation by 12:
12y/12 = 288/12
y = 24
Therefore, Lauren can order 24 steak dinners within her budget if she chooses to order only steak dinners.