Mathematics

Question

the diffrence of two numbers,a and b,is 21,the diffrence of five times a and two times b is 18 what are the values of a and b

2 Answer

  • Answer:

    a=-8

    b=-29

    Step-by-step explanation:

    Let's assume

    first number is a

    second number is b

    the difference of two numbers,a and b,is 21

    so, we get

    [tex]a-b=21[/tex]

    we can solve for 'a'

    [tex]a=b+21[/tex]

    the difference of five times a and two times b is 18

    so, we get

    [tex]5a-2b=18[/tex]

    now, we can plug 'a'

    [tex]5(b+21)-2b=18[/tex]

    now, we can solve for b

    [tex]5b+105-2b=18[/tex]

    [tex]3b+105=18[/tex]

    [tex]3b=-87[/tex]

    [tex]b=-29[/tex]

    now, we can find 'a'

    [tex]a=-29+21[/tex]

    [tex]a=-8[/tex]


  • Answer:

    Values of a and b are;

    a = -8 and b  = -29

    Step-by-step explanation:

    As per the statement:

    Difference of two numbers, a and b is 21

    i.e,  a -b = 21                      .......[1]

    Also, it is given that the difference of five times a and two times b is 18.

    "five times a" means 5a

    "two times b" means 2b

    then;

    5a - 2b = 18                        ......[2]

    We can write equation [1] as;

    a = b + 21                           .....[3]

    Substitute the value of a in equation [2] we have;

    [tex]5(b+21)-2b =18[/tex]

    Using distributive property;  [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]

    5b + 105 - 2b = 18

    combine like terms we get;

    3b = 18 -105

    Simplify:

    3b = -87

    Divide by 3 on both sides we get;

    b = -29

    Substitute the value of b in equation [3] to solve for a;

    a = -29 + 21 = -8

    Therefore, the values of a and b is, -8 and -29

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