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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTwo friends visited a taffy shop. Rachel bought 22 kilograms of strawberry taffy and 55 kilograms of banana taffy for $43\$43. Next, Devon bought 11 kilogram of strawberry taffy and 11 kilogram of banana taffy for $11\$11. How much does the candy cost?\newlineA kilogram of strawberry taffy costs $\$_____, and a kilogram of banana taffy costs $\$_____.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineTwo friends visited a taffy shop. Rachel bought 22 kilograms of strawberry taffy and 55 kilograms of banana taffy for $43\$43. Next, Devon bought 11 kilogram of strawberry taffy and 11 kilogram of banana taffy for $11\$11. How much does the candy cost?\newlineA kilogram of strawberry taffy costs $\$_____, and a kilogram of banana taffy costs $\$_____.
  1. Equations Setup: Let's denote the cost of a kilogram of strawberry taffy as SS dollars and the cost of a kilogram of banana taffy as BB dollars. We can write two equations based on the information given:\newline11. For Rachel's purchase: 2S+5B=432S + 5B = 43\newline22. For Devon's purchase: S+B=11S + B = 11
  2. Elimination Method: To solve the system using elimination, we want to eliminate one of the variables. We can multiply the second equation by 22 to align the coefficients of SS:2(S+B)=2(11)2(S + B) = 2(11)2S+2B=222S + 2B = 22
  3. New System of Equations: Now we have a new system of equations:\newline11. 2S+5B=432S + 5B = 43\newline22. 2S+2B=222S + 2B = 22\newlineWe can subtract the second equation from the first to eliminate SS:\newline(2S+5B)−(2S+2B)=43−22(2S + 5B) - (2S + 2B) = 43 - 22
  4. Subtraction to Eliminate S: Performing the subtraction gives us:\newline2S+5B−2S−2B=43−222S + 5B - 2S - 2B = 43 - 22\newline5B−2B=215B - 2B = 21\newline3B=213B = 21
  5. Solving for B: Dividing both sides of the equation by 33 to solve for B:\newline3B3=213\frac{3B}{3} = \frac{21}{3}\newlineB=7B = 7\newlineSo, a kilogram of banana taffy costs $7\$7.
  6. Substitute BB to Find SS: Now that we know the cost of banana taffy, we can substitute B=7B = 7 into one of the original equations to find SS. We'll use the second equation:\newlineS+B=11S + B = 11\newlineS+7=11S + 7 = 11
  7. Substitute B to Find S: Now that we know the cost of banana taffy, we can substitute B=7B = 7 into one of the original equations to find SS. We'll use the second equation:\newlineS+B=11S + B = 11\newlineS+7=11S + 7 = 11Subtracting 77 from both sides to solve for SS:\newlineS+7−7=11−7S + 7 - 7 = 11 - 7\newlineS=4S = 4\newlineSo, a kilogram of strawberry taffy costs $4\$4.

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