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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 g; nickel: 4.967 g; dime: 2.316 g. What is the maximum number of sets that can be assembled from 33.871 kg of quarters, $10.432 \mathrm{kg}$ of nickels, and $7.990 \mathrm{kg}$ of dimes? What is the total mass (in g) of the assembled sets of coins?

The total number of sets is 1725The total mass of the assembled sets is $4.576 \cdot 10^{4}$

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

University of Maryland - University College

Brown University

University of Toronto

Lectures

02:29

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications.

04:42

In chemistry and physics, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles and objects that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (known as phases) that are defined by various physical properties, such as state of matter, phase, shape, and density. The Standard Model of particle physics and the general theory of relativity describe fundamental particles and the fundamental forces acting between them that control the structure and dynamics of matter.

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A bank teller is asked to …

09:12

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Coins The combined mass of…

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for this question we have to first determine how many of each coin that we have. So given the masses of the coins and kilograms. So we have to convert it to grams because that's what we need to answer to bid. So 1000 g or one kg You know how to convert from kg. two g multiplied by thousands. So we move the decimal .3 places to the right. So every done this version we get this as the masses of the different coins. Now we want to determine number of each of the coins that we have because that's going to determine how many steps we can make. So we're just going to take our mass and grams divided by mass in grams of one of the coins. And then we're just going to drop the decimal portion because we can't have a decimal portion of a coin. So For the first one we get 6000, Then for the next one We get 2100. Then for the next one we're going to drop whatever after the decimal place. So if you type this into the calculator, you'll see that We get 3,449.91 something Dimes. But we can't have .91 of a dime. So we're just going to drop that part, we get 3,449 times. I'll also keep in mind that if these are counted numbers, they don't really count for significant figures because counter numbers don't really matter with significant figures. So now we have determined the number of sets we can make. So one of the coins is going to limit the number of sets we're going to make. So each sect Because this is 3/4 one nickel at one time. So we divide the number of each coin we have by the number of coins Of that coin we need in one set. So we see that out with the 6000 quarters. We can make 2000 sets with the 2100 nickels. We can make 2100 sets. But with the dimes we can only make 1700 24 sets. So we're limited by the number of times that we have. We can only make 1724 sets. So if we have that many stats, we have to multiply by the number of coins and also the mass of each coin. So we have 1724 sets. So we're going to multiply the number of sets by 3/4 because each quarter. Each set contains 3/4 and then multiplied by the mass of one quarter. And we can get the mass that's contributed by the quarters too. Besets. So we're going to do the same for nickel And each side has one nickel and then we do the same for the dimes. So it has two dimes. Then we end up getting the masses that are contributed from each of the coins. Now we want the total mass. We're just going to add them together. So when we add these together, technically the first number, it has four significant figures. So that's our last significant digit. So you can see that we have to follow the rules of addition and subtraction. So because this technically had, this is the last thing. If you figure, we're going to also report this to the same place value and We get 45,740 g as the final answer.

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