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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• 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

• 4200= 42*100

42=7*6

100=10*10

70,60

• 6*7=42, 14*3=42

60*70=4200140*30=4200

• 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.

• 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

• 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.

• 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

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