Question

Upperloaf Bakery is baking loaves of corn bread and poppy-seed blueberry cake. The recipe for one loaf of corn bread calls for 2 (1/4) cups of flour and 1 (1/4) teaspoon of baking soda. One loaf of poppy-seed blueberry cake requires 1 3/4 cups of flour and 2 (1/8) teaspoons of baking soda. The bakery has 28 cups of flour and 30 teaspoons of baking soda in stock. Write a system of two inequalities to model loaves of bread and cake that can be baked then graph the inequalities that represent how many loaves of each type of bread and cake the bakers.

Answer 1

To model the number of loaves of corn bread and poppy-seed blueberry cake that can be baked, write a system of inequalities based on the available flour and baking soda. Graph the inequalities to find the feasible region.

Step-by-step explanation:

To write a system of inequalities to model the number of loaves of corn bread and poppy-seed blueberry cake that can be baked, we need to consider the limitations on the available flour and baking soda.

Let's define:

x = number of loaves of corn bread

y = number of loaves of poppy-seed blueberry cake

The inequalities can be written as:

2 (1/4) * x + 1 1/4 * y ≤ 28 - represents the available cups of flour

1 3/4 * x + 2 1/8 * y ≤ 30 - represents the available teaspoons of baking soda

To graph these inequalities, we can first convert them to slope-intercept form, and then plot the corresponding lines on a coordinate plane. The feasible region where the two lines overlap will represent the values of x and y that satisfy both inequalities.