Question

Kenneth bought 15 chicken sandwiches and tuna sandwiches for $35.10. Each chicken sandwich costs $2.30 and each tuna sandwich costs $2.40. How many chicken sandwiches did Kenneth buy?

Help! Can you do a guess and check? Awarding 20 points!

NONSENSE=REPORT​

Answer 1

the number of chicken sandwiches = 9

Explanation:

let x be the number of chicken sandwiches

y be the number of tuna sandwiches

We have to solve this system:

`\begin{cases}x+y=15&\\ 2.3x+2.4y=35.1&\end{cases}`

`\Longleftrightarrow \begin{cases}y=15-x&\\ 2.3x+ 2.4(15-x)=35.1&\end{cases}`

`\Longleftrightarrow \begin{cases}y=15-x&\\ 2.3x+ 36 -2.4x=35.1&\end{cases}`

`\Longleftrightarrow \begin{cases}y=15-x&\\ -0.1x + 36=35.1&\end{cases}`

`\Longleftrightarrow \begin{cases}y=15-x&\\ -0.1x=-0.9&\end{cases}`

`\Longleftrightarrow \begin{cases}y=15-x&\\ x = 9&\end{cases}`

`\Longleftrightarrow \begin{cases}y=15-9=6&\\ x = 9&\end{cases}`