Sample Question With Problem: This Is What I Need A Tour Gro

Sample Question With Problem This Is What I Needa Tour Group Split In

Sample Question With Problem This Is What I Needa Tour Group Split In

This assignment involves solving a problem related to the cost of pizza slices and soft drinks using elimination method in systems of equations. The problem states that a tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for $36.12. The second group bought 6 slices of pizza and 6 soft drinks for $31.74. The task is to determine the cost of one slice of pizza, and further, to find the cost of a soft drink by substituting the value.

The equations are set up as follows: Let x = the cost of a slice of pizza, y = the cost of a soft drink. Then:

  • 8x + 4y = 36.12
  • 6x + 6y = 31.74

To eliminate y, multiply the first equation by 3 and the second by 2, then subtract. This yields:

  • 24x + 12y = 108.36
  • 12x + 12y = 63.48

Subtracting the second from the first: 12x = 44.88, then divided by 12 gives x = 3.74, the cost of a single slice of pizza. To find the cost of a soft drink, substitute x into one of the original equations:

8(3.74) + 4y = 36.12, which simplifies to 29.92 + 4y = 36.12. Subtract 29.92: 4y = 6.20, then divide by 4: y = 1.55. The cost of a soft drink is $1.55. The detailed steps involve setting variables, forming equations, and applying elimination to solve for the unknowns.

Paper For Above instruction

This problem exemplifies the application of systems of equations in real-world situations, specifically in determining individual prices from combined purchase data. The beverage and food industry frequently uses such models for pricing strategies. The ability to formulate equations based on given data and choose an appropriate solving method is essential in algebra. Here, elimination proves effective due to the coefficients of y in the equations being multiples of common factors, allowing straightforward subtraction to solve for x. This schematization underscores the importance of understanding the structure of equations before selecting a solution method.

Using the elimination method requires careful coefficient adjustments to align terms for elimination. In this instance, multiplying the equations by factors that equalize the coefficients of y enables subtraction that removes the y variable. The derived value of x, or the pizza slice cost, was obtained by dividing the remaining term by the coefficient of x. Subsequently, substituting x back into an initial equation offers the price of the soft drink, y, completing the solution. Such an approach demonstrates systematic problem-solving in algebra beyond mere guesswork, illustrating its practical utility.

The problem also highlights the importance of setting up equations accurately based on real-world data points and understanding the relationships between different items. Misinterpretation or calculation errors can lead to incorrect solutions, so verifying solutions by back-substitution reinforces their validity. Overall, this problem encapsulates key algebraic principles: translating real-world context into mathematical models and solving those models systematically to derive specific information.

References

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