Math Problem Statement

A beverage is sold in three different sizes: small, medium, and large. If Bonar buys 3 small packages, 2 medium packages, and 2 large packages, the total volume amounts to 4,700 ml. You are asked to: a) Write the system of equations. b) Determine if the system is linear. c) Solve the system and find the volume for each package size. d) How many solutions does this system have? e) What does the solution mean in terms of the beverage sizes?

Solution

The image contains a word problem related to a system of linear equations. Let's break down the question and solve it step-by-step.

Problem Outline:

  1. A beverage is sold in three different sizes: small, medium, and large.
  2. Bonar buys three small packages, 2 medium packages, and 2 large packages.
  3. The total volume from these purchases equals 4,700 ml.
  4. The task is to determine: a. The volume of each size. b. Whether the system of equations for this scenario is linear. c. The total number of solutions for the system.

Let's set up the equations based on the variables:

  • Let x represent the volume of the small package.
  • Let y represent the volume of the medium package.
  • Let z represent the volume of the large package.

We are given the following relationships:

  1. 3x+2y+2z=47003x + 2y + 2z = 4700 ml (the total volume of all packages purchased).
  2. The volumes for the small, medium, and large packages are 1,000 ml, 1,500 ml, and 2,000 ml, respectively.

Next, let's derive the solution:

Step 1: Set up the equations

  • Small: x=1000x = 1000 ml
  • Medium: y=1500y = 1500 ml
  • Large: z=2000z = 2000 ml

Step 2: Solve the equation for volume.

Substituting into the equation 3x+2y+2z=47003x + 2y + 2z = 4700: 3(1000)+2(1500)+2(2000)=47003(1000) + 2(1500) + 2(2000) = 4700 3000+3000+4000=47003000 + 3000 + 4000 = 4700 10000=470010000 = 4700 This equation does not hold true, so there may be an inconsistency in the problem setup.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
System of Linear Equations

Formulas

3x + 2y + 2z = 4700

Theorems

Fundamental theorem of systems of linear equations

Suitable Grade Level

Grades 9-11