A bank teller is asked to assemble sets of coins for his clients. Each set is made up of three

step 1 We're given the following information. A bank teller is asked to assemble $1 sets of coins, and

A bank teller is asked to assemble sets of coins for his...

A bank teller is asked to assemble $$\$1$$ sets of coins for his clients. Each set is made up of three quarters, one nickel, and two dimes. The masses of the coins are quarter, $5.645 \mathrm{~g}$; nickel, $4.967 \mathrm{~g}$; and dime, $2.316 \mathrm{~g}$. What is the maximum number of complete sets that can be assembled from $33.871 \mathrm{~kg}$ of quarters, $10.432 \mathrm{~kg}$ of nickels, and $7.990 \mathrm{~kg}$ of dimes? What is the total mass (in grams) of the assembled sets of coins?

Key Concepts

Total Mass Calculation

After identifying the number of complete sets that can be constructed, the total mass of the assembled sets is found by multiplying the mass of one complete set by the number of sets. This aggregation step is vital for determining overall quantities or weights in similar optimization or resource allocation problems.

Limiting Resource

In problems involving multiple components, the overall production is restricted by the component that is available in the least sufficient amount relative to its required usage per set. This component, known as the limiting resource, dictates the maximum number of complete sets that can be assembled.

Unit Conversion

Before performing any calculations, it is essential to work with consistent units. In many real-world problems, quantities may be given in different units (for example, kilograms and grams). Converting all measurements to a common unit ensures that arithmetic operations such as multiplication and division can be carried out accurately.

Per-Set Component Requirement

This concept involves identifying the quantity of each component required for one complete set or unit. By breaking down the problem into how much of each part is needed per unit, one can later determine how many complete sets can be built from the available resources.

Division for Maximum Set Determination

Determining the maximum number of complete sets involves dividing the total available amount of each component by its corresponding per-set requirement. This step is crucial because it shows how many sets each resource can support independently before any one of them runs out.

Transcript

Please give Ace some feedback