Applications of Linear Equations Monetary Word Problem

In summary, the problem given is that Lorraine has $7.70 in dimes and quarters, with the number of quarters being two more than twice the number of dimes. The goal is to find the number of each type of coin she has. After some trial and error, the solution is found to be 12 dimes and 26 quarters. However, the professor requires showing work in order to receive credit, so the person is struggling to come up with a working formula. They have attempted to use a formula from class, but it does not seem to be working. They are seeking help to find a solution.
  • #1
dajohu
2
0
Hi,
This is the problem:
Lorraine has $7.70 in dimes and quarters. If the number of quarters is two more than twice the number of dimes, how many of each type does she have?
I know the answer is 12 dimes and 26 quarters by figuring it in my head, but my professor requires us to show work to get credit of course and I can't come up with a working formula.
What I have so far figured is this:
25x + 20x + 20 + 10x - 10x = 770
45x = 750
x = 16.666... To me this won't work and I've been working on it for quite a while and can't really figure out what I'm doing wrong. I am using a formula that the professor went over in class, but like many other times, the problems we go over in class aren't quite like what we have for homework. I would appreciate any help anyone could offer.
Thanks
 
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  • #2
Let y be the number of dimes and x be the number of quarters. Then

[tex]25x + 10y = 770[/tex]

and

[tex]x=2y+2.[/tex]

Now just solve~
 
  • #3
Thanks!

Thanks a bunch, I don't know why I couldn't figure that out, I really appreciate your help.
-dajohu :smile:
 

What is a linear equation?

A linear equation is an algebraic equation with the form y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope, and b is the y-intercept. It represents a straight line on a graph and is used to model relationships between two variables.

How are linear equations used in monetary word problems?

Linear equations are used in monetary word problems to model the relationship between the amount of money earned or spent and the number of items purchased. These equations can be used to determine the cost per item, the total cost, and the break-even point.

What is the break-even point in a monetary word problem?

The break-even point is the point at which the total revenue equals the total cost. In other words, it is the point at which the amount of money earned is equal to the amount of money spent. This point is important in determining profitability and making financial decisions.

How do you solve a monetary word problem using linear equations?

To solve a monetary word problem using linear equations, you will first need to identify the relevant variables, such as the cost per item, the number of items, and the total cost. Then, you can set up a linear equation using the given information and solve for the unknown variable. It is important to check your answer to ensure it makes sense in the context of the problem.

What are some real-life applications of linear equations in finance?

Linear equations have many real-life applications in finance, including budgeting, investing, and loan repayment. They can also be used in analyzing trends and making predictions in the stock market. In addition, linear equations are used in businesses to determine pricing strategies and optimize profits.

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