Going to the game, solving equations in word problems

Question

Betty purchased two hotdogs and one soda for $11. Jose and his family purchased two hotdogs and three sodas for $17. Write an equation for Betty's purchase using "h" for the price of the hotdog and "d" for the price of the soda. Do the same for Joses purchase. Determine the cost of a hotdog and a soda"

Answer 1

This involves setting up a system of linear equations.

 

Using the info given in the problem, Betty's purchase can be expressed by:

 

2h + d = 11

 

In addition, Jose's purchase can be expressed as:

 

2h + 3d = 17

 

We now have a system of two equations with two unknowns, which can be solved by using either the Substitution Method or the Elimination Method. Let's use the Substitution Method by solving the first equation for d.

 

2h + d = 11

 

d = 11 - 2h

 

Now, we can replace every instance of d in the second equation with the expression (11 - 2h)

 

2h + 3(11 - 2h) = 17

 

We now have an equation in terms of one variable, which we can easily solve. You should be able to handle the rest, Cynthia, in order to determine the price of a hot dog and the price of a soda.