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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA boutique in Arcadia specializes in leather goods for men. Last month, the company sold 8787 wallets and 5555 belts, for a total of $8,287\$8,287. This month, they sold 4343 wallets and 3636 belts, for a total of $4,713\$4,713. How much does the boutique charge for each item?\newlineThe boutique charges $____\$\_\_\_\_ for a wallet, and $____\$\_\_\_\_ for a belt.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA boutique in Arcadia specializes in leather goods for men. Last month, the company sold 8787 wallets and 5555 belts, for a total of $8,287\$8,287. This month, they sold 4343 wallets and 3636 belts, for a total of $4,713\$4,713. How much does the boutique charge for each item?\newlineThe boutique charges $____\$\_\_\_\_ for a wallet, and $____\$\_\_\_\_ for a belt.
  1. Define variables: Let's define the variables: Let w w be the price of a wallet and b b be the price of a belt.
  2. Write equations: Write the equations based on the information given: \newline11. For last month: 87w+55b=8287 87w + 55b = 8287 \newline22. For this month: 43w+36b=4713 43w + 36b = 4713
  3. Multiply equations: Multiply the first equation by 3636 and the second by 5555 to align the coefficients for elimination:\newline11. 87w×36+55b×36=8287×36 87w \times 36 + 55b \times 36 = 8287 \times 36 \newline22. 43w×55+36b×55=4713×55 43w \times 55 + 36b \times 55 = 4713 \times 55
  4. Perform multiplication: Perform the multiplication:\newline11. 3132w+1980b=298332 3132w + 1980b = 298332 \newline22. 2365w+1980b=259215 2365w + 1980b = 259215
  5. Subtract equations: Subtract the second equation from the first to eliminate b b :\newline3132w+1980b−(2365w+1980b)=298332−259215 3132w + 1980b - (2365w + 1980b) = 298332 - 259215
  6. Simplify equation: Simplify the equation:\newline767w=39117 767w = 39117
  7. Solve for w: Solve for w w :\newlinew=39117767 w = \frac{39117}{767}

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