Phone Bills, Rental Cars and Classifieds

Lump and Per Problems

What’s a Lump and Per Problem?

Certain types of charges are always calculated with a lump sum payment plus a ‘per’ charge

• per minute (phone bill)

• per mile (rental car)

• per word (classified ads)

What’s the equation?

In general, the equation for these charges is in the form:

Cost = Per ( n ) + Lump

Where n is the number of minutes, miles, hours, words, etc.

Sample questions

Sue pays 14.99 a month plus .20 a minute for her long distance. What will her bill be if she talks for 30 minutes this month?

Cost = Per ( n ) + Lump

Lump = 14.99

Per = .20

n = 30Cost = .20 ( 30 ) + 14.99

= 6.00 + 14.99

= 20.99

Sample questions

Sprint charges 14.99 a month plus .20 a minute and MCI charges 12.99 a month plus .25 a minute.

If you don’t talk much, MCI is a better deal because the lump sum is lower.

If you talk a lot, Sprint is the better deal because the charge per minute is lower.

How many minutes a month do you have to talk before Sprint is a better deal?

Sample questions

Sprint charges 14.99 a month plus .20 a minute and MCI charges 12.99 a month plus .25 a minute.

Let’s find out when the two costs are equal.

.20m + 14.99 = .25m + 12.99

-12.99 + 14.99 = .25m - .20m

2.00 = .05m

40 = m

40 minutes is the break-even point.

What is a break-even point?If 40 minutes is the break-

even point, that means that if you talk exactly 40 minutes, the two plans would cost the same.

If you plan to talk less than 40 minutes a month, get the plan with the lower lump sum.

If you talk plan to talk more than 40 minutes a month, you’re better off with the plan with the cheaper minutes.

What if the lump includes minutes?

If your 14.99 includes 30 free minutes and then you pay .50 a minute, what is the charge for talking 2 hours in a month?

Since the first 30 minutes are included (not really free) you’ll only have to pay for 90 minutes of your 2 hours.

Cost = .50 ( 90 ) + 14.99

= 45.00 + 14.99

= 59.99 Ouch!

The stupidest problem I’ve ever seen!

Bill is renting a U-Haul to move to his new house. He has $80.00 budgeted for the move. If the truck costs 30.00 a day plus .50 a mile, how far can he go?

80.00 = .50m + 30.00

80.00 – 30.00 = .50m

50.00 = .50m

100 = m

The stupidest problem I’ve ever seen!

If the truck costs 30.00 a day plus .50 a mile, how far can he go?

Bill can drive the U-Haul 100 miles for $80.00.

And then what?

He unloads his furniture on the highway?

Have these textbook authors never lived in the real world?

Making a Stupid Problem Better

Bill is renting a U-Haul to move to his new house. He has $80.00 budgeted for the move. If the truck costs 30.00 a day plus .50 a mile, and his new house is 150 miles away, has he budgeted enough for the trip? If not, how much more does he need?

Cost = .50m + 30.00

= .50 ( 150 ) + 30.00

= 75.00 + 30.00

= 105.00 He’s 25.00 short.

Making a Life Easier

Calculating costs before driving your U-Haul down life’s highway helps you avoid making costly mistakes.

Math actually can come in handy sometimes!

Lump and Per Problems

All lump and per problems are essentially the same.

Cost = per ( n ) + lump

Per is the cost per whatever

n is the whatever - minutes, hours, miles, words, etc.

lump is the flat charge that you pay regardless of how long, far etc. you go.