The River View Bakery is making peanut butter cookies and loaves of quick bread. The preparation and baking times for each are given in the table below.
Cookies
(per batch) Bread
(per loaf)
Preparation 20 min 10 min
Baking 10 min 30 min
For these two items the owners have allotted 800 minutes of employee time and 900 minutes of baking time.
3. Write a system of equations to illustrate the situation. Use x for the number of batches of cookies and y for the loaves of bread.
I need help on this problem please.
To solve this problem, we need to write a system of equations that represent the given information.
Let's use x to represent the number of batches of cookies and y to represent the number of loaves of bread.
The preparation time for a single batch of cookies is 20 minutes, so the total preparation time for x batches of cookies is 20x minutes.
The preparation time for a single loaf of bread is 10 minutes, so the total preparation time for y loaves of bread is 10y minutes.
The baking time for a single batch of cookies is 10 minutes, so the total baking time for x batches of cookies is 10x minutes.
The baking time for a single loaf of bread is 30 minutes, so the total baking time for y loaves of bread is 30y minutes.
According to the problem, the total employee time allotted is 800 minutes, so the total preparation time and baking time for both the cookies and bread cannot exceed 800 minutes. Therefore, we can write the first equation as follows:
20x + 10y ≤ 800
Similarly, the total baking time allotted is 900 minutes, so the total baking time for both the cookies and bread cannot exceed 900 minutes. Therefore, we can write the second equation as follows:
10x + 30y ≤ 900
So, the system of equations representing the given situation is:
20x + 10y ≤ 800
10x + 30y ≤ 900
These equations describe the constraints on the number of batches of cookies (x) and the number of loaves of bread (y) based on the allotted employee and baking time.