A shop owner spent $540 to purchase a stock of computer keyboards. If the price of each keyboard had been reduced by $2, he could have bough

Question

A shop owner spent $540 to purchase a stock of computer keyboards. If the price of each keyboard had been reduced by $2, he could have bought 3 more keyboards. Find the price of one keyboard.​

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Helga 3 years 2021-09-05T03:29:14+00:00 2 Answers 104 views 0

Answers ( )

  1. yenoanh
    0
    2021-09-05T03:30:17+00:00
    Reply

    Answer:

    Price before discount = $20 per keyboard

    Price after discount = $18 per keyboard

    Before the discount, you can buy 27 keyboards. After the discount, you can buy 30 keyboards.

    ===============================================

    Work Shown:

    k = cost of one keyboard before the price reduction

    540/k = amount of keyboards purchased before the price reduction

    k-2 = cost of one keyboard after the price reduction

    540/(k-2) =  amount of keyboards purchased after the price reduction

    540/(k-2) = (540/k) + 3

    ————–

    If you multiply both sides by the LCM k(k-2), then you’ll clear out the fractions and we can solve for k like so

    540/(k-2) = (540/k) + 3

    540k = 540(k-2) + 3k(k-2)

    540k = 540k – 1080 + 3k^2 – 6k

    0 = 540k – 1080 + 3k^2 – 6k – 540k

    0 = 3k^2 – 6k – 1080

    3k^2 – 6k – 1080 = 0

    3(k^2 – 2k – 360) = 0

    k^2 – 2k – 360 = 0

    (k – 20)(k + 18) = 0

    k-20 = 0 or k+18 = 0

    k = 20 or k = -18

    We ignore the negative result because a negative price doesn’t make sense.

    ————–

    If k = 20, then

    540/k = 540/20 = 27

    Meaning that you can buy 27 keyboards before the price reduction

    In other words, (27 keyboards)*(20 dollars per keyboard) = 540 dollars total.

    After the price reduction, the cost per keyboard is now k-2 = 20-2 = 18

    We can now buy 540/(k-2) = 540/18 = 30 keyboards, which is an increase of 30-27 = 3 extra keyboards. This helps confirm we have the correct answer.  

  2. Verity
    0
    2021-09-05T03:30:51+00:00
    Reply

    Answer:

    $20

    Step-by-step explanation:

    X: the price of a keyboard

    Y: number of keyboards to buy (original)

    The shop owner spent $540 to purchase a stock of computer keyboards, so:

    XY=540

    ⇒X=540/Y

    If the price of each keyboard had been reduced by $2, he could have bought 3 more keyboards:

    (X-2)(Y+3)=540  

    ⇒3X-2Y=6

    ⇒3.540/Y – 2Y=6

    ⇒Y=27

    ⇒X=20

    ⇒ the price of one keyboard: $20

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