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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 152A
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 X H ^ i n > i ^ a f t ^ ^ l ^ ^ l a % T ^ 2CO W - s
Then c l O X = ^ ^ ( ^ C C j cWdj^^AM
Equation: +
constantcost moneyspenton additional texts total text cost
AO
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 additional hour, how many hours did you work total if you got paid $165 that day?
Let = m >^Wr.^ y Y A A f e i m V v A a ^ c ^ bV\ctvrs Then i^x - fivynfiVt W r ( V x L ^ r b
Equation: (^) III constant payment payment for additional hours total payment
- ^ ^ ^ -\Cv>U^ 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 minute 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 = w ItMu^o g -y r i \i .v ^m^ \ccm '5Dcn Then ^fj^,XK = fo^^HXi {-
And ^mtK = f(mn (^^P ^p \r **
Equation: ^ t.^\ fi^H.ACX V V fixed cost+moneyspent on minutesuscd fixed cost+moneyspenl on minutesused
7^
Answer: (^200) = number of mmutes 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 )C = 5d\ % (\ir£r>c g ^in^9 ^ c c c v t v ^ ^ Then 5 C C ^ = V T ^ C V ^ And iaX;t.C))e = ^y^is^ ^ V ^^tj "~ Equation: 'X^Ul^ = JCCX t.QJX fixed salary+salary made from sales fixed salary+salary made from sales
o P < K ^ s e c
c 0 \ 0 \
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? ' y^^^^^^^'^)
Let ji_= imiir \iikmr&^nVxi)^<-£^^
Equation: ,
lstroom'.sarea 2nd room'sarea 3rd room'sarea total area
Answer: 80 sq. ft. = area of T' and 2"*^ 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, aniJ^.Yiolet each spend?
L e t ^ - VVl^A -y^x^ ,r , r c ^ = ^ ^ ^ £ ^
Then = PyAbt '^(^ ''^^K3C-^50)
And X-t-^O = rnm^AJMyrWis^roV 2 ^
Equation: < + ^/x + X f-T = \ . (^) V J (^) V J \ V V SHazeispent SRubyspent SVioletspent totalSspent
C6 _ <^ _
Answer: $200 = $ Hazel spent $800 = $ Ruby spent $250 = $ Violet spent
