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

Question

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

roderick_young · Answer

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

charlatan · Answer

4200= 42*100
42=7*6
100=10*10
70,60

Philomel · Answer

6*7=42, 14*3=42

60*70=4200140*30=4200

Pinkgreen · Answer

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.

? · Answer

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

? · Answer

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.

Puzzling · Answer

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)

Captain Matticus, LandPiratesInc · Answer

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

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

8 Answers