Systems Of Equations: A Vendor Sells Hot Dogs And Bags Of Po

Systems Of Equations1 A Vendor Sells Hot Dogs And Bags Of Potato Chip

Solve the following system of equations to find the cost of each item:

A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot dogs and 4 bags of potato chips for $9.25. Find the cost of each item.

Formulate the system of equations where x represents the cost of a hot dog and y represents the cost of a bag of potato chips:

4x + 5y = 12.00

3x + 4y = 9.25

Using substitution or elimination method, solve the system to determine the individual costs of hot dogs and potato chips.

Paper For Above instruction

The problem involves determining the individual prices of two commodities: hot dogs and potato chips, based on transactional data involving different purchase combinations. This practical scenario illustrates how systems of linear equations can model real-life situations where multiple unknowns are involved, and multiple conditions are given.

Let's first translate the problem into a system of equations. Let x denote the price of a hot dog, and y denote the price of a bag of potato chips. Based on the provided data, we have:

  • First customer: 4 hot dogs and 5 bags of chips for $12.00, which gives the equation 4x + 5y = 12.00.
  • Second customer: 3 hot dogs and 4 bags of chips for $9.25, which yields 3x + 4y = 9.25.

To solve this system, it is convenient to use either the substitution or elimination method. Here, the elimination method can be straightforward. Multiply the first equation by 3 and the second by 4 to align the coefficients of x:

First equation x 3: 12x + 15y = 36

Second equation x 4: 12x + 16y = 37

Subtract the first from the second to eliminate x:

(12x + 16y) - (12x + 15y) = 37 - 36

which simplifies to:

y = 1

With y determined as 1 (meaning each bag of potato chips costs $1), substitute y = 1 into the first original equation to find x:

4x + 5(1) = 12

4x + 5 = 12

4x = 7

x = 1.75

Thus, the hot dog costs $1.75, and the bag of potato chips costs $1.00.

This example demonstrates the utility of systems of equations in solving everyday problems involving multiple unknowns. Finding the individual costs allows vendors to price products accurately and helps consumers understand the value of their purchases.

References

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