Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To address this question, we need to investigate two different aspects. First, we need to check if the organic prices of the listed foods vary directly with their conventional prices. If they do, there should be a constant ratio, denoted by [tex]\( k \)[/tex], between the organic price and the conventional price for each food item. Second, we will discern whether the total cost of organic apples varies directly with the number of pounds purchased. If that is the case, we also need to find the value of [tex]\( k \)[/tex].
### Checking Direct Variation between Organic and Conventional Food Prices
When two quantities vary directly, their ratio is constant. To determine if the organic prices vary directly with the conventional prices, we compute the ratio [tex]\( k \)[/tex] for each food item.
#### Calculating Ratios [tex]\( k \)[/tex]:
1. Carrots:
[tex]\[ k_{\text{carrots}} = \frac{\$1.51 \, / \, \text{lb}}{\$0.77 \, / \, \text{lb}} = 1.961038961038961 \][/tex]
2. Apples:
[tex]\[ k_{\text{apples}} = \frac{\$2.34 \, / \, \text{lb}}{\$1.57 \, / \, \text{lb}} = 1.4904458598726114 \][/tex]
3. Onions:
[tex]\[ k_{\text{onions}} = \frac{\$1.57 \, / \, \text{lb}}{\$0.93 \, / \, \text{lb}} = 1.6881720430107527 \][/tex]
#### Determining Consistency of Ratios:
We observe the three computed ratios:
[tex]\[ k_{\text{carrots}} = 1.961038961038961, \quad k_{\text{apples}} = 1.4904458598726114, \quad k_{\text{onions}} = 1.6881720430107527 \][/tex]
Since these ratios are not equal, there is no constant [tex]\( k \)[/tex] that can describe the relationship between the organic and conventional prices for all listed foods. Therefore, the organic prices do not vary directly with the conventional prices.
### Checking Direct Variation of Total Cost of Organic Apples with Pounds Purchased
The total cost of a product when purchased varies directly with the number of pounds if the cost per pound is constant. This scenario holds true for the organic apples.
1. The cost per pound for organic apples is \$2.34.
2. Therefore, if [tex]\( x \)[/tex] denotes the number of pounds of organic apples purchased, the total cost [tex]\( C \)[/tex] is given by:
[tex]\[ C = 2.34 \times x \][/tex]
The total cost varies directly with the number of pounds [tex]\( x \)[/tex], with the constant [tex]\( k \)[/tex] being:
[tex]\[ k = 2.34 \][/tex]
### Summary
1. The organic prices do not vary directly with the conventional prices because the ratios are not consistent across the food items.
2. The total cost of organic apples does vary directly with the number of pounds of organic apples purchased, with the constant [tex]\( k = 2.34 \)[/tex].
### Checking Direct Variation between Organic and Conventional Food Prices
When two quantities vary directly, their ratio is constant. To determine if the organic prices vary directly with the conventional prices, we compute the ratio [tex]\( k \)[/tex] for each food item.
#### Calculating Ratios [tex]\( k \)[/tex]:
1. Carrots:
[tex]\[ k_{\text{carrots}} = \frac{\$1.51 \, / \, \text{lb}}{\$0.77 \, / \, \text{lb}} = 1.961038961038961 \][/tex]
2. Apples:
[tex]\[ k_{\text{apples}} = \frac{\$2.34 \, / \, \text{lb}}{\$1.57 \, / \, \text{lb}} = 1.4904458598726114 \][/tex]
3. Onions:
[tex]\[ k_{\text{onions}} = \frac{\$1.57 \, / \, \text{lb}}{\$0.93 \, / \, \text{lb}} = 1.6881720430107527 \][/tex]
#### Determining Consistency of Ratios:
We observe the three computed ratios:
[tex]\[ k_{\text{carrots}} = 1.961038961038961, \quad k_{\text{apples}} = 1.4904458598726114, \quad k_{\text{onions}} = 1.6881720430107527 \][/tex]
Since these ratios are not equal, there is no constant [tex]\( k \)[/tex] that can describe the relationship between the organic and conventional prices for all listed foods. Therefore, the organic prices do not vary directly with the conventional prices.
### Checking Direct Variation of Total Cost of Organic Apples with Pounds Purchased
The total cost of a product when purchased varies directly with the number of pounds if the cost per pound is constant. This scenario holds true for the organic apples.
1. The cost per pound for organic apples is \$2.34.
2. Therefore, if [tex]\( x \)[/tex] denotes the number of pounds of organic apples purchased, the total cost [tex]\( C \)[/tex] is given by:
[tex]\[ C = 2.34 \times x \][/tex]
The total cost varies directly with the number of pounds [tex]\( x \)[/tex], with the constant [tex]\( k \)[/tex] being:
[tex]\[ k = 2.34 \][/tex]
### Summary
1. The organic prices do not vary directly with the conventional prices because the ratios are not consistent across the food items.
2. The total cost of organic apples does vary directly with the number of pounds of organic apples purchased, with the constant [tex]\( k = 2.34 \)[/tex].
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
