Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The student council at Belleville High School is raising money by selling hot apple cider and hot chocolate at this week's games. They sold 16 apple ciders and 74 hot chocolates at the football game, raising a total of $180. They raised $138 at the soccer game by selling 42 apple ciders and 27 hot chocolates. How much is the student council selling each drink for? The student council is selling apple cider for $_____ and hot chocolate for $_____.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  The student council at Belleville High School is raising money by selling hot apple cider and hot chocolate at this week's games. They sold 16 apple ciders and  74 hot chocolates at the football game, raising a total of $180. They raised $138 at the soccer game by selling 42 apple ciders and  27 hot chocolates. How much is the student council selling each drink for?  The student council is selling apple cider for $_____ and hot chocolate for $_____.

Bytelearn · Accepted Answer

Identify Equations: Identify the equations based on the information given. First game sales: Apple ciders sold: 16 Hot chocolates sold: 74 Total raised: $180 Let x be the price of one apple cider and y be the price of one hot chocolate. The equation for the first game sales is: 16x + 74y = 180Second Game Sales: Identify the equation for the second game sales. Second game sales: Apple ciders sold: 42 Hot chocolates sold: 27 Total raised: $138 The equation for the second game sales is: 42x + 27y = 138Eliminate Variable: Choose which variable to eliminate. We have two equations: 16x + 74y = 180 42x + 27y = 138 To eliminate one variable, we can multiply the first equation by a number that will make the coefficient of x or y in the first equation equal to the coefficient in the second equation. Let's choose to eliminate y.Common Coefficient: Find a common coefficient for y. We need to find a number that both 74 and 27 are divisible by. Since there is no such number, we can multiply the equations by the coefficients of y from the other equation to create a common coefficient. We can multiply the first equation by 27 and the second equation by 74 to get: 16x * 27 + 74y * 27 = 180 * 27 42x * 74 + 27y * 74 = 138 * 74New Equations: Write the new equations after multiplication. Multiplying the first equation by 27: 432x + 1998y = 4860 Multiplying the second equation by 74: 3108x + 1998y = 10212Subtract Equations: Subtract the second equation from the first to eliminate y. (432x + 1998y) - (3108x + 1998y) = 4860 - 10212 432x - 3108x + 1998y - 1998y = 4860 - 10212 -2676x = -5352Solve for x: Solve for x. Divide both sides by -2676 to find the value of x: x = -5352 / -2676 x = 2Substitute for y: Substitute the value of x into one of the original equations to solve for y. Using the first original equation: 16x + 74y = 180 16(2) + 74y = 180 32 + 74y = 180 74y = 180 - 32 74y = 148Solve for y: Solve for y. Divide both sides by 74 to find the value of y: y = 148 / 74 y = 2Final Answer: State the final answer. The student council is selling apple cider for $2 and hot chocolate for $2.

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