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A basketball team stopped at a fast-food restaurant after a game. They are divided into two groups. One group bough 5 chicken sandwiches and 7 hamburgers for a cost of
$24.90. The second group spent
$28.80 and bought 5 chicken sandwiches and 9 hamburgers. Write a system of equations to represent the situation. Then use it to find the cost of each chicken sandwich and each hamburger?

A basketball team stopped at a fast-food restaurant after a game. They are divided into two groups. One group bough $5$ chicken sandwiches and $7$ hamburgers for a cost of $\$ 24.90$ . The second group spent $\$ 28.80$ and bought $5$ chicken sandwiches and $9$ hamburgers. Write a system of equations to represent the situation. Then use it to find the cost of each chicken sandwich and each hamburger?

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Solve a system of equations using elimination: word problems

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Q. A basketball team stopped at a fast-food restaurant after a game. They are divided into two groups. One group bough

5

chicken sandwiches and

7

hamburgers for a cost of

\$ 24.90

. The second group spent

\$ 28.80

and bought

5

chicken sandwiches and

9

hamburgers. Write a system of equations to represent the situation. Then use it to find the cost of each chicken sandwich and each hamburger?

Write Equations: Write the system of equations based on the orders of the two groups. $\newline$ Group $1$ : $5$ chicken sandwiches and $7$ hamburgers for $\$24.90$ . $\newline$ Group $2$ : $5$ chicken sandwiches and $9$ hamburgers for $\$28.80$ . $\newline$ Let $x$ be the cost of a chicken sandwich and $y$ be the cost of a hamburger. $\newline$ The equations are: $\newline$ $5x + 7y = 24.90$ (Equation $1$ ) $\newline$ $5x + 9y = 28.80$ (Equation $2$ )
Use Elimination: Use elimination to solve the system of equations. $\newline$ We can eliminate $x$ by subtracting Equation $1$ from Equation $2$ . $\newline$ $(5x + 9y) - (5x + 7y) = 28.80 - 24.90$ $\newline$ $5x + 9y - 5x - 7y = 28.80 - 24.90$ $\newline$ $2y = 3.90$
Solve for y: Solve for y, the cost of a hamburger. $\newline$ $2y = 3.90$ $\newline$ $y = \frac{3.90}{2}$ $\newline$ $y = 1.95$ $\newline$ So, each hamburger costs $\$1.95$ .
Substitute and Solve: Substitute the value of $y$ into one of the original equations to solve for $x$ , the cost of a chicken sandwich. $\newline$ Using Equation $1$ : $\newline$ $5x + 7(1.95) = 24.90$ $\newline$ $5x + 13.65 = 24.90$ $\newline$ $5x = 24.90 - 13.65$ $\newline$ $5x = 11.25$ $\newline$ $x = \frac{11.25}{5}$ $\newline$ $x = 2.25$ $\newline$ So, each chicken sandwich costs $\$2.25$ .

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