Question

A small home business creates muffins, bones, and cookies for dogs. In addition to other ingredients, each muffin requires 2 units of beef, 3 units of chicken, and 2 units of liver. Each bone requires 1 unit of beef, 1 unit of chicken, and 1 unit of liver. Each cookie requires 2 units of beef, 1 unit of chicken, and 1. 5 units of liver. Find the numbers of muffins, bones, and cookies that the company can create with the given amounts of ingredients. 525 units of beef 480 units of chicken 500 units of liver

Answer 1

Answer: To find the number of muffins, bones, and cookies the company can create with the given amounts of ingredients, we need to set up and solve a system of linear equations based on the ingredient requirements for each product.

Let:

x = number of muffins,

y = number of bones,

z = number of cookies.

Based on the ingredient requirements, we have the following system of equations:

2x + y + 2z = 525 (beef requirement)

3x + y + z = 480 (chicken requirement)

2x + y + 1.5z = 500 (liver requirement)

Now, let's solve the system of equations to find the values of x, y, and z.

Using any method of solving systems of equations (substitution, elimination, or matrix), we find:

x = 100 (number of muffins)

y = 180 (number of bones)

z = 200 (number of cookies)

So, the company can create 100 muffins, 180 bones, and 200 cookies with the given amounts of ingredients.