Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To determine which values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] fit within the librarian's budget and maximize the number of DVDs purchased, we can evaluate each combination provided. Remember, [tex]\( x \)[/tex] represents the number of new-release movies at [tex]\( \$20 \)[/tex] each and [tex]\( y \)[/tex] represents the number of classic movies at [tex]\( \$8 \)[/tex] each. The budget is [tex]\( \$500 \)[/tex].
We need to calculate the total expenditure for each combination and check if it is within the budget.
### Combination 1: [tex]\( x = 8 \)[/tex], [tex]\( y = 45 \)[/tex]
[tex]\[ \text{Total Cost} = (8 \times 20) + (45 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 160 + 360 = 520 \][/tex]
This combination exceeds the budget of [tex]\( \$500 \)[/tex].
### Combination 2: [tex]\( x = 10 \)[/tex], [tex]\( y = 22 \)[/tex]
[tex]\[ \text{Total Cost} = (10 \times 20) + (22 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 200 + 176 = 376 \][/tex]
This combination is within the budget of [tex]\( \$500 \)[/tex].
### Combination 3: [tex]\( x = 16 \)[/tex], [tex]\( y = 22 \)[/tex]
[tex]\[ \text{Total Cost} = (16 \times 20) + (22 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 320 + 176 = 496 \][/tex]
This combination is also within the budget of [tex]\( \$500 \)[/tex].
### Combination 4: [tex]\( x = 18 \)[/tex], [tex]\( y = 18 \)[/tex]
[tex]\[ \text{Total Cost} = (18 \times 20) + (18 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 360 + 144 = 504 \][/tex]
This combination exceeds the budget of [tex]\( \$500 \)[/tex].
### Conclusion
The combinations that fit within the [tex]\( \$500 \)[/tex] budget are:
- [tex]\( x = 10 \)[/tex], [tex]\( y = 22 \)[/tex] with a total cost of [tex]\( \$376 \)[/tex]
- [tex]\( x = 16 \)[/tex], [tex]\( y = 22 \)[/tex] with a total cost of [tex]\( \$496 \)[/tex]
Thus, the possible combinations that the librarian can afford are:
[tex]\[ (10, 22) \quad \text{and} \quad (16, 22) \][/tex]
We need to calculate the total expenditure for each combination and check if it is within the budget.
### Combination 1: [tex]\( x = 8 \)[/tex], [tex]\( y = 45 \)[/tex]
[tex]\[ \text{Total Cost} = (8 \times 20) + (45 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 160 + 360 = 520 \][/tex]
This combination exceeds the budget of [tex]\( \$500 \)[/tex].
### Combination 2: [tex]\( x = 10 \)[/tex], [tex]\( y = 22 \)[/tex]
[tex]\[ \text{Total Cost} = (10 \times 20) + (22 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 200 + 176 = 376 \][/tex]
This combination is within the budget of [tex]\( \$500 \)[/tex].
### Combination 3: [tex]\( x = 16 \)[/tex], [tex]\( y = 22 \)[/tex]
[tex]\[ \text{Total Cost} = (16 \times 20) + (22 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 320 + 176 = 496 \][/tex]
This combination is also within the budget of [tex]\( \$500 \)[/tex].
### Combination 4: [tex]\( x = 18 \)[/tex], [tex]\( y = 18 \)[/tex]
[tex]\[ \text{Total Cost} = (18 \times 20) + (18 \times 8) \][/tex]
[tex]\[ \text{Total Cost} = 360 + 144 = 504 \][/tex]
This combination exceeds the budget of [tex]\( \$500 \)[/tex].
### Conclusion
The combinations that fit within the [tex]\( \$500 \)[/tex] budget are:
- [tex]\( x = 10 \)[/tex], [tex]\( y = 22 \)[/tex] with a total cost of [tex]\( \$376 \)[/tex]
- [tex]\( x = 16 \)[/tex], [tex]\( y = 22 \)[/tex] with a total cost of [tex]\( \$496 \)[/tex]
Thus, the possible combinations that the librarian can afford are:
[tex]\[ (10, 22) \quad \text{and} \quad (16, 22) \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.