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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineWestminster City Cafe recently introduced a new flavor of coffee. They served 6565 grande cups and 3030 jumbo cups of the new coffee today, which equaled a total of 41,17541,175 grams. The day before, 6565 grande cups and 3131 jumbo cups were served, which used a total of 41,70941,709 grams. How much coffee is required to make each size?\newlineThere are _\_ grams in a grande cup of coffee and _\_ grams in a jumbo one.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineWestminster City Cafe recently introduced a new flavor of coffee. They served 6565 grande cups and 3030 jumbo cups of the new coffee today, which equaled a total of 41,17541,175 grams. The day before, 6565 grande cups and 3131 jumbo cups were served, which used a total of 41,70941,709 grams. How much coffee is required to make each size?\newlineThere are _\_ grams in a grande cup of coffee and _\_ grams in a jumbo one.
  1. Equation 11: Let's denote the amount of coffee required for a grande cup as 'gg' grams and for a jumbo cup as 'jj' grams.\newlineThe first equation comes from the first day's servings: 6565 grande cups and 3030 jumbo cups made a total of 41,17541,175 grams.\newlineSo, the equation is: 65g+30j=41,17565g + 30j = 41,175.
  2. Equation 22: The second equation comes from the second day's servings: 6565 grande cups and 3131 jumbo cups made a total of 41,70941,709 grams.\newlineSo, the equation is: 65g+31j=41,70965g + 31j = 41,709.
  3. System of Equations: We now have a system of equations:\newline11) 65g+30j=41,17565g + 30j = 41,175\newline22) 65g+31j=41,70965g + 31j = 41,709\newlineWe can solve this system by subtracting the first equation from the second to eliminate 'gg'.
  4. Subtracting Equations: Subtracting the first equation from the second gives us:\newline(65g+31j)−(65g+30j)=41,709−41,175(65g + 31j) - (65g + 30j) = 41,709 - 41,175\newlineThis simplifies to:\newline65g+31j−65g−30j=41,709−41,17565g + 31j - 65g - 30j = 41,709 - 41,175\newlineWhich further simplifies to:\newlinej=534j = 534
  5. Solving for j: Now that we have the value for 'j', we can substitute it back into one of the original equations to solve for 'g'.\newlineLet's use the first equation: 65g+30j=41,17565g + 30j = 41,175.\newlineSubstituting 'j' with 534534 gives us:\newline65g+30(534)=41,17565g + 30(534) = 41,175.
  6. Substitute and Solve for g: Now we solve for 'g':\newline65g+16,020=41,17565g + 16,020 = 41,175\newline65g=41,175−16,02065g = 41,175 - 16,020\newline65g=25,15565g = 25,155\newlineg=25,15565g = \frac{25,155}{65}\newlineg=387g = 387

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