find two parts of 15 such that the sum of their reciprocals is 3/10​

find two parts of 15 such that the sum of their reciprocals is 3/10​

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Claire

2 thoughts on “find two parts of 15 such that the sum of their reciprocals is 3/10​”

  1. ✍️A᭄NSWER✍️

    ʟᴇᴛ ᴛʜᴇ ᴛᴡᴏ ᴘᴀʀᴛs ʙᴇ x ᴀɴᴅ x − 15.

    [tex] \frac{1}{x} + \frac{1}{15 – x} = \frac{3}{10} [/tex]

    [tex] \frac{15 – x + x}{x(15 – x} = \frac{3}{10} [/tex]

    [tex] \frac{15}{15x – {x}^{2} } \ = \frac{3}{10} [/tex]

    ➪ 150 = 145 – 3x^2

    ➪ 3x^2 – 45x + 150 = 0

    ➪ x^2 – 15x + 150 = 0

    ➪ (x-5) (x-10)

    ➪ x = 5 , 10

    x = 5

    ⟹ ᴏɴᴇ ᴘᴀʀᴛ = 5 ᴀɴᴅ ᴏᴛʜᴇʀ ᴘᴀʀᴛ = 10 x = 10

    ⟹ ᴏɴᴇ ᴘᴀʀᴛ = 10 ᴀɴᴅ ᴏᴛʜᴇʀ ᴘᴀʀᴛ = 5 ᴛʜᴜs,

    ᴛʜᴇ ʀᴇǫᴜɪʀᴇᴅ ᴛᴡᴏ ᴘᴀʀᴛs ᴀʀᴇ 5 ᴀɴᴅ 10.

    ╚─━━━━━░★░━━━━━─╝

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  2. Step-by-step explanation:

    first condition

    x+y=15____(1)

    by second condition

    1/x + 1/y = 3/10

    3x + 3y =10____(2)

    multiply equation (1) by 3

    3x+3y = 45____(3)

    add and subtract equation (2) & (3)

    addition: 6x+6y = 55___(4)

    subtraction :o=35_____(5)

    add (4)&(5)

    6x+6y = 90

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