Assign two variables for each problem, and write the equations. do not solve.
a pair of boots and a pair of tennis shoes cost $196.12. the difference in their cost is $44.38. determine the cost of each type of shoe.
do not say 'just divide' or 'just multiply' the two numbers. i need the two variables and two equations.

Price of boots is represented as x, price of tennis shoes is represented as y. x-y=44.38 x+y=196.12 Isolate x. (Or y, if you wanted to) x=y+44.38 x=196.12-y Set them equal to each other. y+44.38=196.12-y Solve for y. Then plug it in to either of the two original equations to find x. x=120.24 y=75.86 Note: This is assuming that the boots are more expensive than the tennis shoes. If the tennis shoes are more expensive than the boots, then the prices would be switched. I didn't find this clear in your question.