Question

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?

Name: Problem 206, Chapter 5: Elementary Algebra
Uploaded: 2021-07-29T03:23:31-08:00
Duration: 2 min 36 s
Channel: Melissa Barry
Description: 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?

   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?

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 5, Problem 206

Instant Answer

Solved by Expert Melissa Barry

07/29/2021

Step 1

Set up equations from the purchases: 7o + 3b = 17 3o + 6b = 12 Show more…

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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?

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Key Concepts

Elimination Method

This is a common technique used to solve a system of linear equations. It involves manipulating the equations such that adding or subtracting them cancels out one of the variables, making it easier to solve for the remaining one. Once one variable is found, it can be substituted back into one of the original equations to find the other.

Systems of Linear Equations

This concept involves setting up multiple equations that represent different conditions or scenarios, where each equation includes the same set of unknown variables. In problems like this, each scenario (such as a purchase with given weights and total cost) provides an equation, and together they form a system that can be solved simultaneously to find the values of the unknowns.

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