Question

One of your new friends is on your flight home to the United Kingdom! At the airport snack stand, you buy one hot pretzel and one bottle of water for $2.10. Your friend buys 2 hot pretzels and 3 bottles of water for $5.15. How much does the pretzel cost? How much does a bottle of water cost Solve Using Elimination

Answer 1

`pretzel=\: \$1.15,\: water\colon\: \$0.95`

1) In this question, let's for the first part set the equations. Gathering the data:

You | your friend

1 hot pretzel 2 pretzels

1 bottle of water 3 bottles of water

$2.10 $5.15

2) Setting the equations we have, calling "p" for pretzels and "w" for water bottles:

p+w=2.10 Referring to my consumption

2p +3w =5.15 Referring to my friend's purchase

3) So, now let's set the system and solve it by the Elimination Method as requested, let's multiply the first equation by -2

`\begin{gathered} \mleft\{\begin{matrix}p+w= & 2.10 \\ 2p+3w= & 5.15 \\ \end{matrix}\mright. \\ \mleft\{\begin{matrix}-2p-2w= & -4.20 \\ 2p+3w= & 5.15 \\ \end{matrix}\mright. \\ --------------- \\ w=0.95 \end{gathered}`

Now that we know the price of the water bottle, let's plug it into the first original equation and solve it for "p":

`\begin{gathered} p+0.95=2.1 \\ p=2.1-0.95 \\ p=1.15 \end{gathered}`