A store is having a sale on choculate chips and walnuts. For 2 pounds of chocolate chips and 5 pounds of walnuts, the total cost is \( \$ 18 \). For 8 pounds of chocolate chips and 3 pounds of walnuts, the total cost is \( \$ 21 \). Find the coet for each pound of chocolate chips and each pound of walnuts. Cost for each pound of chocolate chips: \( \$ 1.50 \) poch pound of walnuts: \( 5 \square \)
Upstudy AI Solution
Answer
Solution
Answered by UpStudy AI and reviewed by a Professional Tutor
Explain 
Simplify this solution The Deep Dive
To solve this classic system of equations, we can first set up our equations based on the given information. Let \( x \) represent the cost per pound of chocolate chips and \( y \) the cost per pound of walnuts. From the problem, we have: 1. \( 2x + 5y = 18 \) 2. \( 8x + 3y = 21 \) By solving these equations using substitution or elimination, we find that the cost per pound of chocolate chips is \( \$ 1.50 \) and for walnuts, it concludes to \( \$ 2.00 \) per pound! Understanding how to set up and solve systems of equations can be super beneficial. This skill not only applies to shopping scenarios like this but also in budgeting, finance, and even in fields like engineering or data analysis, where balancing multiple variables is crucial. Want to avoid common mistakes in such problems? Always double-check your initial equations for accuracy, and when manipulating them, pay close attention to signs—positive and negative—since they can change the entire solution. Plotting the equations can also help visualize where they intersect, leading you to the solution more intuitively!
