Practice #10

Below are two practice problems. Solve one of them using the substitution method and one using the addition/subtraction method. You can choose which problem to solve using substitution, and which to solve using addition/subtraction.

1. Suppose we have the equations of two lines, which represent the supply and demand of a product. Where the two lines intersect they have equality, which represents equilibrium in the market. (See the graph below.) Calculate the value of x, D, and S at the equilibrium point, i.e., when S = D.

   S = (1/100)x + 2 D = (–1/100)x + 8

2. John leaves his house and drives west at 40mph. Sam lives 25 miles west of John and leave his house at the same time as John. Sam is traveling 30mph. John catches up with Sam after John has driven D miles. The distance driven by John is given by 40t = D. The distance Sam drives, D – 25, is given by 30t = D –25, where t is the amount of time they drive. Find out how long they drove, and the distance John traveled.

   ---

   
   [Solution to Practice]