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Chapter 2.
Steps for Solving Application Problems:
- Read, throw out nonsense numbers
- Assign a variable (What is it asking for?)
- Write an equation
- Solve the equation
- Check, does it make sense?
Math 233A
Chapter 2.3: Solving Application Problems
Objectives:
- Fixed cost plus cost/percent per something
- Finding when fixed cost plus cost/percent per something is equal to a different fixed cost plus cost/percent per something
- Leaving a tip
- The sum of three items Fixed Costs Plus Additional Costs
Ex: M y cell phone plan charges $5 for 200 text messages and then $.10 for each additional text. If I was billed $18.50 for texting, how many text messages did I use?
Let Then
Equation: (^) + constantcost moneyspenton additional texts total text cost
Answer: 135 = number of texts used after the first 200 335 = number of total texts You try:
- If you got paid a flat rate of $120 for the first 8 hours on a job and $18/hr for each addifional hour, how many hours did you work total if you got paid $165 that day?
Let = Then
Equation: + = ^ V ' ^ V ^ ^ V constant pa>'nient pa>'menl for additional hours total payment
Answer: 2.5 = number of hours worked after 8 hours 10.5 = total hours worked
Finding When a Fixed Cost Plus Additional Costs is Equal to a Different Fixed Cost Plus Additional Costs
Ex: Company A has a monthly cell phone plan that charges a flat rate of $49 and $.30 for each mmute used and Company B has a monthly cell phone plan that charges a flat rate of $89 and $. 10 for each minute used. How many minutes would you have to use for both plans to cost the same?
Let = Then = And =
Equation: = V V fixed cost+moneyspenton minutesused fixedcost+moneyspenlon minutesused
Answer: 200 = number of minutes used for both plans to cost the same
You try:
- Commission job A pays a fixed salary of $500 plus 2% of sales (money you make for the company) and commission job B a fixed salary of $1000 plus 1% of sales. How much in sales would you have to make for both jobs to pay the same salary? Let = Then = And = Equation: = fixed salary+salary made from sales fixed salary+salary made from sales
Answer: $50,000 = amount made in sales for both companies to pay the same salary
Sum of Three Items
Ex: A house for sale has 2 bedrooms with the same square footage, and a third bedroom that is 4 sq. ft. less than five times the area of the other two rooms. Together, all three rooms have a total of 556 sq. ft. How much area does each room have?
Let = Then = Equation:
+ _+ =
_\ \ ^ i _ 1 si room'sarea 2ndroom'sarea 3rd room'sarea tola) area
Answer: 80 sq. ft. = area of and room 396 sq. ft. = area of 3"^ room You try: \ Ruby, Hazel, and Violet went shopping and spent a total of $1250. If Ruby spent 4 times as much as Hazel, and Violet only spent $50 more than Hazel, how much did Ruby, Hazel, and Violet each spend?
Let = Then = And =.
Equation: +^ +^ =^ ^ ^/ V ^ SHazelspent SRubyspent SVioletspent totalSspent
Answer: $200 = money Hazel spent $800 = money Ruby spent $250 = money Violet spent
