Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

a × b = 4,200. If a and b are two-digit multiples of 10, what numbers could a and b represent?

a × b = 4,200. If a and b are two-digit multiples of 10, what numbers could a and b represent?

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  • 2 months ago

    both are multiples of 10

    so a = 10x , where x is a value we will find later

    b = 10y

    ab = 4200

    a * 10 * b * 10 = 4200

    a * b = 42

    It says "two digit," so a and b must be integers.

    The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

    To make a 2-digit number, a and b must be single digits, leaving us with

    1, 2, 3, 6, and 7.

    There is only one pair out of these that multiplies to 42.  Those are the values for x and y, then add a 0 to each to get a and b.

    If your class has learned negative numbers already, then there is also a pair of negative numbers that answers the question: -60 and -70

  • 2 months ago

    4200= 42*100

    42=7*6

    100=10*10

    70,60

  • 2 months ago

    6*7=42, 14*3=42

    60*70=4200140*30=4200

  • ?
    Lv 7
    2 months ago

    Let a=10x, b=10y, where x,y are integers.

    ab=4200

    =>

    xy100=4200

    =>

    xy=42=6*7

    =>

    x=6

    y=7

    =>

    a=60.

    b=70.

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  • ?
    Lv 7
    2 months ago

    a × b = 4,200. 

    If a and b are two-digit multiples of 10, 

    what numbers could a and b represent?

    a = 70, b = 60

  • ?
    Lv 7
    2 months ago

    a and b are two-digit multiples of 10.

    a = 10x

    b = 10y

    where x and y are single digit numbers.

    10x * 10y = 4200

    x * y = 42

    Factor pairs of 42 are:

    1 and 42

    2 and 21

    3 and 14

    6 and 7

    Only the last is two single digit numbers.

  • 2 months ago

    The possible choices for a and b are 10, 20, 30, ..., 90

    Assuming m and n are single digits (1 to 9), then:

    a = 10m

    b = 10n

    a × b = 4200

    10m × 10n = 4200

    mn = 4200 / 100

    mn = 42

    The only way to factor 42 into a pair of single digit factors is 6 × 7 = 42 or 7 × 6 = 42

    Answer:

    a and b are 60 and 70, in some order.

    (a = 60, b = 70 or a = 70, b = 60)

  • a = 10x

    b = 10y

    10x * 10y = 4200

    100xy = 4200

    xy = 42

    We know that x and y are both single digit (since 10x was 2 digits, as was 10y)

    x * y = 42

    Divisors of 42:

    1 , 2 , 3 , 6 , 7 , 14 , 21 , 42

    1 * 42

    2 * 21

    3 * 14

    6 * 7

    Which one fits the bill?

    a = 10x

    b = 10y

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