Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Band students at Arcadia High School sell candy every year as a fundraiser. Last year, they sold 69 boxes of truffles and 89 boxes of peanut brittle, raising a total of $454. This year, they sold 73 boxes of truffles and 99 boxes of peanut brittle, from which they raised $490. How much does the band earn from each item? The band earns $_____ from each box of truffles and $_____ from each box of peanut brittle.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  Band students at Arcadia High School sell candy every year as a fundraiser. Last year, they sold 69 boxes of truffles and 89 boxes of peanut brittle, raising a total of $454. This year, they sold 73 boxes of truffles and 99 boxes of peanut brittle, from which they raised $490. How much does the band earn from each item?  The band earns $_____ from each box of truffles and $_____ from each box of peanut brittle.

Bytelearn · Accepted Answer

Define variables: Define the variables for the cost of each box of truffles (t) and each box of peanut brittle (p).Write equations for last year: Write the system of equations based on the information given for last year's sales. 69 boxes of truffles and 89 boxes of peanut brittle raised $454. 69t + 89p = 454Write equations for this year: Write the system of equations based on the information given for this year's sales. 73 boxes of truffles and 99 boxes of peanut brittle raised $490. 73t + 99p = 490Eliminate variable t: Choose which variable to eliminate. We will eliminate t by multiplying the first equation by -73 and the second equation by 69 to make the coefficients of t opposites. -73(69t + 89p) = -73(454) 69(73t + 99p) = 69(490)Perform multiplication: Perform the multiplication to get the new equations. -5047t - 6497p = -33142 5047t + 6831p = 33810Add equations to eliminate t: Add the two equations together to eliminate t. (-5047t - 6497p) + (5047t + 6831p) = -33142 + 33810 0t + 334p = 668Solve for p: Solve for p. 334p = 668 p = 668 / 334 p = 2Substitute p to solve t: Substitute the value of p back into one of the original equations to solve for t. 69t + 89(2) = 454 69t + 178 = 454 69t = 454 - 178 69t = 276 t = 276 / 69 t = 4

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