Math Homework Help Needed! A Group Of Students Is Organizing
Math Homework Help Needed! A group of students is organizing
A group of students is organizing a bake sale to raise money for their school trip. They plan to sell two types of cookies: chocolate chip cookies and oatmeal cookies. The number of chocolate chip cookies they plan to bake is represented by the variable 'c', and the number of oatmeal cookies is represented by the variable 'o'. The total cost to bake 'c' chocolate chip cookies is given by the expression 0.75c, and the total cost to bake 'o' oatmeal cookies is given by the expression 0.50o.
If the students plan to bake a total of 100 cookies, write an algebraic expression to represent the total cost of baking all the cookies. Also, determine the total cost if they bake 30 chocolate chip cookies and 70 oatmeal cookies. To find the total cost, add the cost of baking chocolate chip cookies to the cost of baking oatmeal cookies.
Paper For Above instruction
The task involves creating an algebraic expression to calculate the total baking cost when students prepare cookies for a school fundraiser. The problem specifies two types of cookies: chocolate chip cookies, denoted by 'c', and oatmeal cookies, denoted by 'o'. The cost per chocolate chip cookie is $0.75, and the cost per oatmeal cookie is $0.50. The primary objective is to formulate an expression representing the total cost based on the number of each type of cookie baked, and then compute this total for specific quantities.
First, to develop the algebraic expression, we consider the individual costs associated with each type of cookie. The total cost of baking 'c' chocolate chip cookies is represented as 0.75c, which accounts for the cost per cookie multiplied by the number baked. Likewise, the total cost for 'o' oatmeal cookies is 0.50o. Since the total cost is the sum of these two individual costs, the general algebraic expression for the total cost (T) can be written as:
T = 0.75c + 0.50o
Next, applying the total number of cookies baked (c + o = 100), we can express either 'c' or 'o' in terms of the other, or simply identify the total cost for specific quantities. For example, if the students bake 30 chocolate chip cookies ('c' = 30) and 70 oatmeal cookies ('o' = 70), the total cost would be calculated by substituting these values into the expression:
T = 0.75(30) + 0.50(70)
Calculating this, we get:
T = 22.50 + 35.00 = $57.50
Therefore, the total cost to bake 30 chocolate chip cookies and 70 oatmeal cookies is $57.50.
This problem demonstrates the application of algebraic expressions in real-world scenarios, specifically in calculating costs based on quantities. The key steps involve formulating the expression based on the cost per item and the number of items, and then substituting given values to find exact totals. Such mathematical modeling is essential in budgeting and resource allocation tasks in various industries, including food services and event planning.
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