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Write a system of two equations in two unknowns for each problem. Solve each system by the method of your choice.Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for $\$ 1.45$ and June bought two books and five magazines for $\$ 1.25$ What was the price of a book and what was the price of a magazine?

book: $\$ 0.25$magazine: $\$ 0.15$

Algebra

Algebra 2

Chapter 4

Systems of Linear Equations

Section 2

The Addition Method

Polynomials

Systems of Equations and Inequalities

Introduction to Algebra

Graph Linear Functions

Write Linear Equations

Linear Equations and Functions

Matrices and Determinants

Johns Hopkins University

University of Washington

Michigan State University

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So in this prop problem, we're told that great ones garage sale. The books are one price and magazines cost another price. And then we're told that Harriet bought some merchandise and June Watts emergencies. But our old typical is to find the price of a book and the price for a magazine. So I'm gonna let V represent the price of a book, and I'm gonna let em represent the price of a magazine. So now let's first look at what, Harriet. But, well, Harriet bought four books and three magazines for a total of a dollar. 45. Someone we added all up, it should equal 1 45 Well, Harry bought four books, so four b represents the total cost for the four books and three magazines. So plus three m Austrian will be the total for the magazines. So for B plus three m equals a dollar. 45 represents what Harriet bought. Well, we're told that June bought two books and five magazines for a dollar 25. So again, the total should equal dollar 25 while June bought two books. So to be and five magazines. So plus five. And now what? We found is a system of equations. So we're gonna solve this. So I'm gonna do this by the addition Method. Nothing cancels right away. But what I'm gonna do is I'm gonna try and get rid of the bees. So I'm gonna multiply the second equation by negative too. So when I do that, I'm going to get negative. For B minus 10 a.m. is equal to negative $2.50. So now I'm gonna bring that first equation down just so it's written together. And now we're gonna add the two equations together because negative for B plus four B cancels. Well, now we have negative 10 m Astrium, which is negative, seven them. And we have negative $2.50 plus a dollar 45 which is negative $1.5. So now when we divide both sides by negative seven, we're going to get 15 cents. So now we know the price of the magazine is 15 cents. Now, we need the price for the books. So to do this, we go back to either of our original equations, so I'm gonna do the 2nd 1 to be plus five M is a dollar 25 but now we know the magazines or 15 cents each. So we're gonna substitute that it. So we have to be plus five times 15 cents is equal to a dollar. 25. Well, five times 15 cents. It's 75 cents. And now we solve for be. So I'm going to subtract 75 cents from both sides, so we're gonna have to be is equal to 50 cents. And when we divide by two, we're gonna find that P is equal to 25 cents, so the cost of a book is 25 cents.

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