Math 152A Chapter 2.3: Solving Appiication 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: My 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 texl cost

Answer: 135 = number of texts used after the first 200 335 = number of total texts

You try: 1. 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 = Then =

Equation: + = constant payment pajTiient for additional hours total payment

Answer: 2.5 = number of hours worked after 8 hours 10.5 = total hours worked

Chapter 2.3 Steps for Solving Application Problems:

1. Read, throw out nonsense numbers 2. Assign a variable (What is it asking for?) 3. Write an equation 4. Solve the equation 5. Check, does it make sense?

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 =

Then =

And =

Equation: ^ = ^ fixed cost+moneyspent on minutesused fixed cost+moneyspentonminutesused

Answer: 200 = number of minutes used for both plans to cost the same

You try: 1. 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+salarj' made from sales

Answer: $50,000 = amount made in sales for both companies to pay the same salary

Leaving a Tip

Ex: Say you only have $26.28, and you want to go to a local restaurant. If you have to pay a 9.5% sales tax and want to leave a 20% tip on the total bill (meal plus tax), what is the maximum price of the meal you can order, what is the cost of the sales tax, and what is the cost of the tip?

Let =

Then =

And =

Equation:

+ + = cost of meal cost of sales tax cost of tip total cost

Answer: $20 = cost of meal before tax and tip $1.90 = cost of sales tax $4.38 = cost of tip

You try: 1. Say you only have $31.05, and you want to go to a local restaurant. If you have to pay an 8% sales tax

and want to leave a 15% tip on the total bill (meal plus tax), what is the maximum price of the meal you can order, what is the cost of the sales tax, and what is the cost of the tip?

Let =

Then =

And =

Equation: + + = costofmeal cost of sales tax costoftip totalcost

Answer: $25 = cost of meal before tax and tip $2 = cost of sales tax

$4.05 = cost of tip

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: + + =

\ ^ / \ \

) Si room'sarea 2ndrooni'sarea 3rdroom'sarea total area

Answer: 80 sq. ft. = area of 1̂^ and 2" room 396 sq. ft. = area of 3"̂ room

You try: 1. 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 V V V

SHazelspcnt SRubyspent SVioletspent totalSspent

Answer: $200 = money Hazel spent $800 = money Ruby spent $250 = money Violet spent