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28 September, 05:22

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.

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  1. 28 September, 06:15
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    p = $2

    q = $1.6

    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
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