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A vegetable stand sells pumpkins for each and squashes for each. On Monday, the stand sold more squashes than pumpkins and made a total of . Which system of equations can be used to determine the number of pumpkins and squashes sold?Choose answer:(A) (B) (C) (D)
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Q. A vegetable stand sells pumpkins for each and squashes for each. On Monday, the stand sold more squashes than pumpkins and made a total of . Which system of equations can be used to determine the number of pumpkins and squashes sold?Choose answer:(A) (B) (C) (D)
- Identify Equations: question_prompt: What system of equations can be used to determine the number of pumpkins ( extit{p}) and squashes ( extit{s}) sold if the stand sold more squashes than pumpkins and made a total of ?
- Write Total Money Equation: Step : Let's write the equation for the total money made from selling pumpkins and squashes. Pumpkins cost each, and squashes cost each. So, the equation is:
- Establish Relationship Equation: Step : Now, we know that the stand sold more squashes than pumpkins. So, the equation for the relationship between the number of squashes and pumpkins sold is:
- Compare with Options: Step : We need to check which answer choice matches our equations. Let's look at the options:(A) , (B) , (C) , (D) , $p = s + \(6\)
- Compare with Options: Step \(3\): We need to check which answer choice matches our equations. Let's look at the options:\(\newline\)(A) \(3p + 5s = 98\), \(s = p + 6\)\(\newline\)(B) \(3p + 5s = 98\), \(p = s + 6\)\(\newline\)(C) \(5p + 3s = 98\), \(s = p + 6\)\(\newline\)(D) \(5p + 3s = 98\), \(p = s + 6\) Step \(4\): By comparing the equations we wrote with the options, we can see that option (C) has the same equations as we derived:\(\newline\)\(5p + 3s = 98\), \(s = p + 6\)
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