Question

For each customer, a bakery charges p dollars for the first loaf of bread bought by the customer and charges q dollars for each additional loaf bought by the customer. What is the value of p ?

(1) A customer who buys 2 loaves is charged 10 percent less per loaf than a customer who buys a single loaf.
(2) A customer who buys 6 loaves of bread is charged 10 dollars.

Answer 1

p = $2

q = $1.6

Step-by-step explanation:

If a customer buys 2 loaves he will pay p for the first and q for the second

p + q

if a customer buys a single loaf he pays p

10% less of p is expressed as

p - 0.1p

1. A customer who buys 2 loaves is charged 10% less per loaf (this means average) than a customer who buys a single loaf is expressed as

(p+q)/2 = (p - 0.1p)

(p+q)/2 = 0.9p

(p + q) = 1.8p (cross multiply so that 2*0.9)

q = 1.8p - p

q= 0.8p (equation 1)

2. If a customer buys 6 loaves of bread he will pay p for the first loaf and q for each of the remaining 5 so that

p + 5q = $10 (equation 2)

Now put substitute equation 1 into 2

p + 5(0.8p) = $10

p + 4p = 10 (add)

5p = 10

p = 2 (after dividing both sides by 5)

Now put p=2 into equation 1

q = 0.8(2)

q = 1.6

Thus p is $2