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James has a collection of nickels and dimes which total to 5.15 dollar. If he has 5 fewer nickels than dimes, how many dimes has he?

$$36$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Missouri State University

University of Michigan - Ann Arbor

Lectures

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Mukul has $\$ 3.75$ in qua…

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Set up an algebraic equati…

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Lee has $\$ 1.75$ in dimes…

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James has $\$ 6$ in dimes …

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Jaime has $\$ 2.60$ in dim…

all right, so we have the following problem or James collects nickels and dimes for up to $5.15 that we're gonna be using a linear equation to solve this. And it's leaner because the unknown value that we're looking for is raised to the power of one. And we're also using the fact that addition and subtraction under each other and multiplication and division also into each other. So James has a total off $5.15 can draw an equation five cents times the number of Nichols he has, plus 10 cents times the number of times that he has is worth up to $5.15 on were given another piece of information. Then he basically has five fewer nickels, then dimes. So if he has five fewer nickels and lines, then that means that end is equal to theme, and it's fine and we're trying to solve for E. We're trying to figure out how many times does James have. So in this equation, we could simply plug in this end value into the original equation and get and solve for deep so we'll just plug in. Yeah, yeah, our end. We'll replace it, right T minus five. And now we're looking at this. And now we're going to distribute the five cents to D and to minus five. So this is gonna be 0.5 and Stevie and this 0.25. Let's see one pretty steep. It's equal to find out this in 15 tons. Now we're gonna add up the points or five D and 50.1 D, which is just 0.15 D. Yeah. Now we're gonna move the 25 cents from the left to the right side. We're going to this by adding 250.25 to both sides of the equation time. This can be 5.15 plus 25 cents. So now we're left with 0.15 times D on the left side is equal to 5.4 on the right side. Now we're going to divide both sides of the equation by 15 cents, or 150.15 or 0.15 Mississippi 5.4 divided by 0.15 We're gonna have the the number of times Beijing says is equal to 36. It's 5.4, divided by 0.15 is 36. So he has 36 times in total. Yeah,

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