Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. At a community barbecue, Mrs. Callahan and Mr. Maynard are buying dinner for their families. Mrs. Callahan purchases 3 hot dog meals and 2 hamburger meals, paying a total of $32. Mr. Maynard buys 2 hot dog meals and 1 hamburger meal, spending $19 in all. How much do the meals cost? Hot dog meals cost $_____ each, and hamburger meals cost $_____ each.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  At a community barbecue, Mrs. Callahan and Mr. Maynard are buying dinner for their families. Mrs. Callahan purchases 3 hot dog meals and 2 hamburger meals, paying a total of $32. Mr. Maynard buys 2 hot dog meals and 1 hamburger meal, spending $19 in all. How much do the meals cost?  Hot dog meals cost $_____ each, and hamburger meals cost $_____ each.

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Equation 1: Mrs. Callahan's purchase: Let's denote the price of each hot dog meal as h and the price of each hamburger meal as d. We can write two equations based on the information given. The first equation comes from Mrs. Callahan's purchase: 3 hot dog meals and 2 hamburger meals for $32, which gives us the equation 3h + 2d = 32.Equation 2: Mr. Maynard's purchase: The second equation comes from Mr. Maynard's purchase: 2 hot dog meals and 1 hamburger meal for $19, which gives us the equation 2h + d = 19.Eliminating variable 'd': We have a system of two equations now. To use elimination, we need to make the coefficients of one of the variables the same in both equations. We decide to eliminate d. To do this, we multiply the second equation by 2 to match the coefficient of d in the first equation, resulting in 4h + 2d = 38.Solving for 'h': Now we subtract the first equation from the new second equation to eliminate d. This gives us (4h + 2d) - (3h + 2d) = 38 - 32, which simplifies to h = 6.Substituting 'h' into Equation 1: With the value of h found, we substitute h = 6 into the first equation to solve for d. Substituting into 3h + 2d = 32 gives us 3(6) + 2d = 32, which simplifies to 18 + 2d = 32.Solving for 'd': Subtracting 18 from both sides of the equation 18 + 2d = 32 gives us 2d = 14. Dividing both sides by 2 gives us d = 7.

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