Math
posted by George .
A home owner goes to the hardware store to purchase the letters that make up a number for a sign he is making, (e.g., FOUR, NINE, etc.). When he arrives, other customers are doing the same thing. The first customer buys the letters to display ONE, and pays $40. The next customer buys the letters for the number TWO, and pays $60. The last customer buys the letters for the number ELEVEN, and pays $100. Our home owner wants to buy the letters to spell out TWELVE.
The question is: how much does the home owner pay?

ok George, I'll play your game.
I will assume that the store owner is some mathnerd and sets the price of the numbers according to some cubic equation
cost = ax^2 + bx + c, where x is the number of letters and a,b,c are constants
so we have three ordered pairs:
(1,40), (2,60) and (11,100)
for (1,40) > a + b + c = 40
for (2,60) > 4a + 2b + c = 60
for (11,100) > 121a + 11b + c = 100
2nd  3rd: > 3a + b = 20
3rd  1st: > 120a + 10b = 60 or 12a + b = 6
subtracting those last two:
9a = 14
a = 14/9
from 12a+b=6
b = 612a = 612(14/9) = 74/3
back in 1st: a+b+c=40
14/9 + 74/3 + c = 40
c = 152/9
so cost = (14/9)x^2 + (74/3)x + 152/9
so when x = 12, Cost = $88.89 
I meant to say:
...according to some quadratic equation
I would need 4 ordered pairs for a cubic.
My work reflects what is needed for a quadratic 
Teacher said answer was $120
Respond to this Question
Similar Questions

Statistics
According to a recent survey, 75% of all customers will return to the same grocery store. Suppose 8 customers are selected at random: A) What is the probability that exactly five of the customers will return? 
marketing
The owner of a small hardware storethe only one in a medium â€“sized town in the mountainshas just learned that a large home improvement chain plans to open a new store nearby. How difficulty will it be for the owner to plan for … 
Combinations
Anna was opening a new restaurant, so she went to the sign store to get letters to make a sign to hang above the storefront. When she got to the sign store, the only letters they had in stock were two copies of the letter 'X,' two … 
Number Theory
Yan was opening a new restaurant, so she went to the sign store to get letters to make a sign to hang above the storefront. When she got to the sign store, the only letters they had in stock were two copies of the letter 'X,' two copies … 
statistics
Fortyfour percent of customers who visit a department store make a purchase. The probability, rounded to four decimal places, that in a random sample of 9 customers who will visit this department store, exactly 6 will make a purchase … 
statistics
Fortyfour percent of customers who visit a department store make a purchase. The probability, rounded to four decimal places, that in a random sample of 9 customers who will visit this department store, exactly 6 will make a purchase … 
math
You make a purchase at a local hardware store, but what you've bought is too big to take home in your car. for a small fee, you arrange to have the hardware store deliver your purchase for you. You pay for your purchase, plus the sales … 
Marketing
The owner of a small hardware storethe only one in a mediumsized town in the mountainshas just learned that a large home improvement chain plans to open a new store nearby. How difficult will it be for the owner to plan for … 
math
A home owner goes to the hardware store to purchase the letters that make up a number for a sign he is making, (e.g., FOUR, NINE, etc.). When he arrives, other customers are doing the same thing. The first customer buys the letters … 
math
The manager of a retail store knows that 40% of the customers who enter the store will purchase one or more items and 60% will leave without making a purchase.what is the probability that in a sample of 10 customers,five will buy one …