Cost of an item

Question

At the food truck Joel bought 3 hot dogs and 4 drinks for $10.Cindy bought 1 hotdog and 3 drinks for $5.Find the cost of each hot dog and each drink 

Answer 1

This problem involves setting up a system of two equations in two variables and solving the system. Let H stand for the cost of each hot dog and D stand for the cost of each drink. Then, using the information from Joel's purchase, you have 3H +4D =10.  From Cindy's purchase, you have 1H +3D =5. Now you can multiply the second equation by 3 to get an equivalent equation of 3H +9D = 15. Then you can subtract the new equation from the first equation, which gives you: (3H-3H) +(4D-9D) = 10-15 . Simplifying, you have -5D =-5 and so D=1. Now you have found that the cost of a drink is $1. Substitute this in either of the original equations for D to get the value of H. I will use the second equation. 1H +3D = 5; 1H +3(1) =5; 1H = 5-3=2. So the cost of one hot dog is $2.

Answer 2

cost of each hot dog =x

cost of each each drink =y

 

3x +4y =10

x +3y =5

 

solve these equation to find the value of x and y