Algebra 2 Math Problem

TL;DR

Learn how to solve a system of linear equations using the elimination method and apply it to find the cost of apples and bananas.

Transcript

here is a question for you if five apples plus nine bananas costs nine dollars and fifty seven cents and nine apples plus six bananas costs 10.80 then how much will six apples and seven bananas cost what is the answer to that question is it a 9.092 c d or e what would you say so feel free to pause the video and take a minute and try this problem if... Read More

Key Insights

• 🍌 The problem involves solving a system of linear equations with two variables: apples and bananas.
• ❓ The elimination method is used to manipulate the equations and eliminate one variable.
• ❓ By substituting the values of the variables back into the original equations, the solution can be verified.
• 🇨🇷 The cost of each apple is found to be $0.78 and the cost of each banana is $0.63.
• ❓ The calculated values satisfy both equations, confirming their accuracy.
• 🍌 The cost of 6 apples and 7 bananas is found to be $9.09.
• 🈸 This problem demonstrates the practical application of systems of equations in determining the cost of multiple items.

Questions & Answers

Q: What method is used to solve the system of linear equations?

The elimination method is used to solve the system of linear equations. This involves manipulating the equations to eliminate one variable and solve for the remaining variables.

Q: How is the elimination method applied in this problem?

The elimination method is applied by multiplying one equation by a suitable multiple and the other equation by a multiple that results in the terms for one variable canceling when the equations are added together.

Q: What are the values of a and b in the system of equations?

The value of a, the cost of each apple, is found to be $0.78. The value of b, the cost of each banana, is found to be $0.63.

Q: How is the cost of 6 apples and 7 bananas calculated?

The cost of 6 apples and 7 bananas is calculated by multiplying the cost of each apple by 6 and the cost of each banana by 7, and then adding the results. In this case, it is found to be $9.09.

Summary & Key Takeaways

• The problem involves finding the cost of apples and bananas based on two equations: 5 apples + 9 bananas = $9.57 and 9 apples + 6 bananas = $10.80.

• By multiplying the equations by suitable multiples and adding them together, one variable can be eliminated, allowing the values of apples and bananas to be calculated.

• The cost of each apple is found to be $0.78 and the cost of each banana is $0.63. Using these values, the cost of 6 apples and 7 bananas is calculated to be $9.09.