Exercise 82 Page 421

We are asked to find the prices for a hot dog, a soda, and a bag of potato chips. Let h, s, and p be these prices of a hot dog, a soda, and a bag of chips, respectively. To find those values we can write a system of equations using the given lunch combinations. First, we know that 2 hot dogs with one soda cost $5.40. 2 h+ s= $5.40 (I) The second combo meal that costs $4.35 contains one hot dog, one soda, and one bag of potato chips. h+ s+ p= $4.35 (II)The last combination is 2 hot dogs and 2 bags of chips, and it costs $5.70. 2 h+ 2 p= $5.70 (III) Now, as we have three variables and three equations, we can write a system of equations and solve it. 2h+s=5.40 & (I) h+s+p=4.35 & (II) 2h+2p=5.70 & (III) Since at least one coefficient is equal to 1, let's use the Substitution Method to solve this system. When using this method it is necessary to isolate a variable. In Equation (I), it will be easiest to isolate s.

With a variable isolated in one of the equations, we can substitute its equivalent expression into Equation (II). In the final step of the simplification of this substitution, our goal is to have yet another variable isolated.

This time, the p-variable was isolated in Equation (II). We can now substitute its equivalent expression into Equation (III).

The value of h is 1.95. Substituting 1.95 for h into Equation (I) and Equation (II), we can find the values of s and p.

The solution to the system is the point ( 1.95, 1.50, 0.90). With this information, we can write the prices of all three products.