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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. Tanvi bought 55 kilograms of strawberry taffy and 55 kilograms of banana taffy for $65\$65. Next, Albert bought 55 kilograms of strawberry taffy and 11 kilogram of banana taffy for $41\$41. 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. Tanvi bought 55 kilograms of strawberry taffy and 55 kilograms of banana taffy for $65\$65. Next, Albert bought 55 kilograms of strawberry taffy and 11 kilogram of banana taffy for $41\$41. 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:\newlineFor Tanvi: 5S+5B=655S + 5B = 65 (Equation 11)\newlineFor Albert: 5S+1B=415S + 1B = 41 (Equation 22)\newlineWe will use these equations to solve for SS and BB using the elimination method.
  2. Elimination Method: To eliminate one of the variables, we can multiply Equation 22 by −5-5 and add it to Equation 11 to eliminate SS.\newlineMultiplying Equation 22 by −5-5 gives us: −25S−5B=−205-25S - 5B = -205 (Equation 33)
  3. Combine Equations: Now we add Equation 11 and Equation 33:\newline(5S+5B)+(−25S−5B)=65+(−205)(5S + 5B) + (-25S - 5B) = 65 + (-205)\newlineThis simplifies to: −20S=−140-20S = -140
  4. Solve for S: We divide both sides of the equation by −20-20 to solve for S:\newline−20S/−20=−140/−20-20S / -20 = -140 / -20\newlineS=7S = 7\newlineSo, a kilogram of strawberry taffy costs $7\$7.
  5. Substitute SS into Equation: Now that we have the value for SS, we can substitute it back into Equation 22 to solve for BB:5(7)+1B=415(7) + 1B = 4135+B=4135 + B = 41
  6. Final Solution: Subtracting 3535 from both sides gives us:\newlineB=41−35B = 41 - 35\newlineB=6B = 6\newlineSo, a kilogram of banana taffy costs $6\$6.

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