Get the answers you've been searching for with IDNLearn.com. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.
Sagot :
I commented on your question but I'll solve it as if the second scenario had 4 hot dogs and 3 hamburgers totaling $13.75
Let D represent hot dogs. Let H represent hamburgers.
[tex]3D+4H=14.25\\ 4D+3H=13.75[/tex]
This is called a system of equations. You must substitute one equation into the other. I'll work it through, and hopefully you can follow along.
[tex]3D+4H=14.25\\ 3D+4H-4H=14.25-4H\\ 3D=14.25-4H\\ \frac{3D}{3}=\frac{14.25}{3}-\frac{4H}{3}\\ D=\frac{19}{4}-\frac{4}{3}H[/tex]
Now you have the value of one hot dog (D). Substitute this value into the other equation. This way you will only be working with the H variable.
[tex]4D+3H=13.75\\ 4(\frac{19}{4}-\frac{4}{3}H)+3H=13.75\\ 19-\frac{16}{3}H+3H=13.75\\ -\frac{16}{3}H+3H=13.75-19\\ -\frac{7}{3}H=-\frac{21}{4}\\ -\frac{7}{3}H*\frac{3}{7}=-\frac{21}{4}*\frac{3}{7}\\ -1H=-\frac{9}{4}\\ H=\frac{9}{4}[/tex]
9/4=2.25 for the price of a Hamburger (H).
Now plug the value for H (2.25) into either equation.
[tex]3D+4H=14.25\\ 3D+4(2.25)=14.25\\ 3D+9=14.25\\ 3D=5.25\\ D=1.75[/tex]
The price for a Hamburger is $2.25
The price for a Hot Dog is $1.75
Let D represent hot dogs. Let H represent hamburgers.
[tex]3D+4H=14.25\\ 4D+3H=13.75[/tex]
This is called a system of equations. You must substitute one equation into the other. I'll work it through, and hopefully you can follow along.
[tex]3D+4H=14.25\\ 3D+4H-4H=14.25-4H\\ 3D=14.25-4H\\ \frac{3D}{3}=\frac{14.25}{3}-\frac{4H}{3}\\ D=\frac{19}{4}-\frac{4}{3}H[/tex]
Now you have the value of one hot dog (D). Substitute this value into the other equation. This way you will only be working with the H variable.
[tex]4D+3H=13.75\\ 4(\frac{19}{4}-\frac{4}{3}H)+3H=13.75\\ 19-\frac{16}{3}H+3H=13.75\\ -\frac{16}{3}H+3H=13.75-19\\ -\frac{7}{3}H=-\frac{21}{4}\\ -\frac{7}{3}H*\frac{3}{7}=-\frac{21}{4}*\frac{3}{7}\\ -1H=-\frac{9}{4}\\ H=\frac{9}{4}[/tex]
9/4=2.25 for the price of a Hamburger (H).
Now plug the value for H (2.25) into either equation.
[tex]3D+4H=14.25\\ 3D+4(2.25)=14.25\\ 3D+9=14.25\\ 3D=5.25\\ D=1.75[/tex]
The price for a Hamburger is $2.25
The price for a Hot Dog is $1.75
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.