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Nancy bought seven pounds of oranges and three pounds of bananas for $\$ 17$. Her husband later bought three pounds of oranges and six pounds of bananas for $\$ 12 .$ What was the cost per pound of the oranges and the bananas?

Algebra

Chapter 5

Systems of Linear Equations

Section 4

Solve Applications with Systems of Equations

Systems of Equations and Inequalities

McMaster University

Baylor University

University of Michigan - Ann Arbor

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in this problem, I want to use a system of equations to determine the cost of £1 of oranges and £1 of bananas. So I'm going to start by assigning the oranges the X. Variable and bananas the Y. Variable. And in the first statement says that £7 of oranges and £3 of bananas 7 $17. So this translates to seven X plus three Y equals 17. The second statement says that £3 of oranges and £6 of bananas is $12. So this translates to three x plus six y equals 12. And I'm going to use the system or a linear method or elimination method to solve this, I'm gonna multiply the first equation by negative two and then I'm gonna rewrite it down here, So this is negative 14 x -6 y Equals -34. And then I'm kind of done with this equation right here. For the time being now I'm gonna add the two bottom equations together. Three x minus 14 X. Is negative 11 X. We eliminated the Y variable in this equals 12 -34 Is -22, Divide by -11 and x equals two. So this means that one of oranges of oranges cost $2. Now that I know that X. Is too I can use that to figure out why. So I'm gonna just use this first equation. So seven times two plus three Y equals 17, 14 plus three Y equals 17. Subtract the 14, 3 Y equals three and divide by three, Y equals one. This means that one lb of bananas equals $1.

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