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Bert made 33 batches of his uncle's signature spicy wing sauce for a barbecue last weekend. He didn't want the sauce to be too spicy, so he tweaked the recipe, reducing the amount of hot sauce he put in each batch by 22 ounces. Bert used 2424 ounces of hot sauce in all to make the wing sauce.\newlineWhich equation can you use to find uu, the amount of hot sauce Bert's uncle usually puts in each batch of spicy wing sauce?\newlineChoices:\newline(A) 2u3=242u - 3 = 24\newline(B) 3(u2)=243(u - 2) = 24\newline(C) 3u2=243u - 2 = 24\newline(D) 2(u3)=242(u - 3) = 24\newlineHow much hot sauce does Bert's uncle usually put in each batch of spicy wing sauce?\newlineWrite your answer as a whole number or a simplified fraction.\newline____ ounces

Full solution

Q. Bert made 33 batches of his uncle's signature spicy wing sauce for a barbecue last weekend. He didn't want the sauce to be too spicy, so he tweaked the recipe, reducing the amount of hot sauce he put in each batch by 22 ounces. Bert used 2424 ounces of hot sauce in all to make the wing sauce.\newlineWhich equation can you use to find uu, the amount of hot sauce Bert's uncle usually puts in each batch of spicy wing sauce?\newlineChoices:\newline(A) 2u3=242u - 3 = 24\newline(B) 3(u2)=243(u - 2) = 24\newline(C) 3u2=243u - 2 = 24\newline(D) 2(u3)=242(u - 3) = 24\newlineHow much hot sauce does Bert's uncle usually put in each batch of spicy wing sauce?\newlineWrite your answer as a whole number or a simplified fraction.\newline____ ounces
  1. Understand the problem: Understand the problem.\newlineBert made 33 batches of wing sauce and reduced the amount of hot sauce by 22 ounces for each batch. He used a total of 2424 ounces of hot sauce. We need to find the original amount of hot sauce used in each batch by Bert's uncle.
  2. Translate the problem: Translate the problem into an equation.\newlineLet uu be the usual amount of hot sauce Bert's uncle puts in each batch. Bert made 33 batches and reduced each by 22 ounces. So, the total amount of hot sauce used by Bert is 33 times the usual amount minus 22 ounces for each batch, which equals 2424 ounces.\newlineThe equation is 3(u2)=243(u - 2) = 24.
  3. Identify the correct equation: Identify the correct equation from the given choices.\newlineThe correct equation that represents the situation is 3(u2)=243(u - 2) = 24, which is choice (B)(B).
  4. Solve the equation for u: Solve the equation for u.\newline3(u2)=243(u - 2) = 24\newlineDivide both sides by 33 to isolate the term with u.\newline(u2)=243(u - 2) = \frac{24}{3}\newline(u2)=8(u - 2) = 8\newlineNow, add 22 to both sides to solve for u.\newlineu=8+2u = 8 + 2\newlineu=10u = 10