Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ At a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases $3$ hot dog meals and $3$ hamburger meals, paying a total of $\$36$ . Mr. Hogan buys $1$ hot dog meal and $3$ hamburger meals, spending $\$26$ in all. How much do the meals cost? $\newline$ Hot dog meals cost $\$$ _ each, and hamburger meals cost $\$$ __ each.

Full solution

Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

At a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases

3

hot dog meals and

3

hamburger meals, paying a total of

\$36

. Mr. Hogan buys

1

hot dog meal and

3

hamburger meals, spending

\$26

in all. How much do the meals cost?

\newline

Hot dog meals cost

\$

_______ each, and hamburger meals cost

\$

________ each.

Define variables: Let's define the variables for the cost of the meals. Let $x$ be the cost of a hot dog meal and $y$ be the cost of a hamburger meal.
Write equations: Write the system of equations based on the information given. Mrs. Wilkerson's purchase gives us the first equation: $3x$ (hot dog meals) + $3y$ (hamburger meals) = $\$36$ . Mr. Hogan's purchase gives us the second equation: $1x$ (hot dog meal) + $3y$ (hamburger meals) = $\$26$ . $\newline$ So we have: $\newline$ $3x + 3y = 36$ $\newline$ $x + 3y = 26$
Solve equations: Solve the system of equations. We can use the substitution or elimination method. Let's use the elimination method. We can multiply the second equation by $-3$ to eliminate $y$ . $\newline$ $-3(x + 3y) = -3(26)$ $\newline$ $-3x - 9y = -78$
Eliminate variable: Now we add the new equation from Step $3$ to the first equation to eliminate $y$ . $(3x + 3y) + (-3x - 9y) = 36 + (-78)$ $3x - 3x + 3y - 9y = 36 - 78$ $0x - 6y = -42$ Since $0x$ is $0$ , we can simplify this to: $-6y = -42$
Solve for y: Solve for y by dividing both sides of the equation by -6＂).$\newline\$-6y / -6 = -42 / -6$$\newline$$y = 7$$\newline$So, the cost of a hamburger meal is $\$7$.
Substitute and solve: Substitute the value of $y$ back into one of the original equations to solve for $x$. We'll use the second equation: $x + 3y = 26$.$x + 3(7) = 26$$x + 21 = 26$$x = 26 - 21$$x = 5$So, the cost of a hot dog meal is $\$5$.