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Chapter 1: Problem 74

A bank teller is asked to assemble "one-dollar" sets of coins for his clients. Each set is made of three quarters, one nickel, and two dimes. The masses of the coins are: quarter: \(5.645 \mathrm{~g}\); nickel: \(4.967 \mathrm{~g}\); dime: \(2.316 \mathrm{~g}\). What is the maximum number of 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 g) of this collection of coins?

Short Answer

Expert verified
The maximum number of 'one-dollar' sets of coins that can be formed and the total mass of this collection can be found using the mentioned steps.

Step by step solution

01

Calculate the number of possible sets each type of coin can form

To begin, we will first calculate how many sets each type of coin can form based on their total mass, and the mass of one coin. We are given total mass of quarters, nickels, and dimes. We will divide the total mass of each type by the mass of one coin to get the number of sets each can form. The formulas are as follows: For quarters: \(\frac{33.871 \times 10^3}{5.645 \times 3}\) (as 3 quarters are needed for a set) For nickels: \(\frac{10.432 \times 10^3}{4.967}\) (as only one nickel is needed for a set) For dimes: \(\frac{7.990 \times 10^3}{2.316 \times 2}\) (as 2 dimes are needed for a set)
02

Find the maximum number of sets that can be assembled

After getting the number of possible coin sets that can be formed by each type, we need to find the maximum number of sets. This will be the smallest number among the sets of quarters, nickels, and dimes as we need all types of coins to form a set.
03

Calculate the total mass of the collection of coins

The total mass of the collection of coins can be calculated by multiplying the number of sets by the mass of one set. Mass of one set is calculated as follows: (3 quarters \(\times\) mass of one quarter) + (1 nickel \(\times\) mass of one nickel) + (2 dimes \(\times\) mass of one dime). So, total mass will be `number of sets \(\times\) mass of one set`

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Most popular questions from this chapter

Which of these properties are intensive and which are extensive? (a) length, (b) volume, (c) temperature, (d) mass.

Convert these to nonscientific notation: (a) \(1.52 \times\) \(10^{4},\) (b) \(7.78 \times 10^{-8}\)

What is the difference between a physical property and a chemical property?

Classify each of these as an element or a compound: (a) sodium chloride (table salt), (b) helium, (c) alcohol, (d) platinum.

A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density \(\left.=0.9986 \mathrm{~g} / \mathrm{cm}^{3}\right)\). The readings are \(860.2 \mathrm{~g}\) and \(820.2 \mathrm{~g}\), respectively. Given that the density of platinum is \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what should her conclusion be based on these measurements? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyancy of air.)
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