Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Dylan and Leo are hosting events that are catered by the same company. Dylan plans to have 87 adults and 96 children attend, so the total projected cost of his meals is $4,938. Leo has 70 adults and 96 children on his guest list, so he will pay the caterer $4,292. How much does the caterer charge for each meal? Every adult's meal costs $_____, and every child's meal costs $_____.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Dylan and Leo are hosting events that are catered by the same company. Dylan plans to have 87 adults and 96 children attend, so the total projected cost of his meals is $4,938. Leo has 70 adults and 96 children on his guest list, so he will pay the caterer $4,292. How much does the caterer charge for each meal?  Every adult's meal costs $_____, and every child's meal costs $_____.

Bytelearn · Accepted Answer

Define Meal Costs: Let's denote the cost of an adult's meal as 'a' and the cost of a child's meal as 'c'. We need to find the values of 'a' and 'c'.Equation for Dylan's Event: Dylan's event has 87 adults and 96 children, and the total cost is $4,938. This gives us the equation: 87a + 96c = 4938Equation for Leo's Event: Leo's event has 70 adults and 96 children, and the total cost is $4,292. This gives us the equation: 70a + 96c = 4292System of Equations: We now have a system of two equations: 1) 87a + 96c = 4938 2) 70a + 96c = 4292 We can solve this system using the method of elimination or substitution. Let's use elimination.Elimination Method: Subtract the second equation from the first to eliminate 'c': (87a + 96c) - (70a + 96c) = 4938 - 4292 17a = 646Solve for 'a': Divide both sides of the equation by 17 to solve for 'a': 17a / 17 = 646 / 17 a = 38Substitute 'a' into Equation: Now that we have the value for 'a', we can substitute it back into one of the original equations to solve for 'c'. Let's use the second equation: 70a + 96c = 4292 70(38) + 96c = 4292Calculate Adults' Total Cost: Multiply 70 by 38 to find the total cost for the adults at Leo's event: 70 * 38 = 2660Calculate Children's Total Cost: Subtract the cost for the adults from the total cost to find the total cost for the children at Leo's event: 4292 - 2660 = 1632Calculate Cost per Child: Now, divide the total cost for the children by the number of children to find the cost per child's meal: 1632 / 96 = 17 c = 17

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