Reconciling a Recreation Center Cash Box Using a System of Equations
At a local municipal recreation center, an assistant coordinator is writing a standard operating procedure (SOP) for reconciling the cash box after swim classes. The box contains only quarters and dimes. To ensure new volunteers can audit the box accurately, the coordinator includes a section on using a system of two linear equations to determine the exact number of each coin.
Suppose the total value in the cash box is 8.55 dollars, and the number of quarters () is 3 more than twice the number of dimes ().
To help the volunteers understand the mathematical structure behind this reconciliation, write a short explanation that addresses the following:
- Identify and describe the two distinct types of equations that must be established to form this system of equations. What physical or monetary quantity does each equation represent?
- Explain the role of the individual coin values (specifically {}0.25 and {}0.10) in these equations, including where they are used as coefficients and why.
- Show how the relationship 'the number of quarters is 3 more than twice the number of dimes' is translated into an equation, and identify which variable is isolated for substitution.
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Intermediate Algebra @ OpenStax
Ch.4 Systems of Linear Equations - Intermediate Algebra @ OpenStax
Algebra
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Cognitive Psychology
Psychology
Social Science
Empirical Science
Science
OpenStax Psychology (2nd ed.) Textbook
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Understanding Coefficients in Coin Value Equations
Reconciling a Recreation Center Cash Box Using a System of Equations