SOLUTION: The product of two two-digit numbers is 1484. The product of their units digits is 24 and the product of their tens digits is 10. The two numbers can be?
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Question 251660: The product of two two-digit numbers is 1484. The product of their units digits is 24 and the product of their tens digits is 10. The two numbers can be? Found 2 solutions by richwmiller, ankor@dixie-net.com:Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website! (10a+b)*(10c+d)=1484
b*d=24
a*c=10
There is not enough info to form 4 equations
but we know that b*d=24
there are only two possible single digit factors
6*4=24
8*3=24
a=2 or a=5
c=2 or c=5
b=6 or b=4
d=6 or d=4
b=8 or b=3
d=8 or d=3
from our equations we know
b = 4 a so must be 8 and a must be 2
8=4*2
a=2 c=5
if a=2 then c must be 5
if b is 4 then d must be 6
a*c=10
b=8 d=3
b*d=24
(10a+b)*(10c+d)=1484
28*53=1484
so the two numbers are 28 and 53
2*5=10
8*3=24
You can put this solution on YOUR website! Here's another way to do this.
:
The product of two two-digit numbers is 1484.
The product of their units digits is 24 and the product of their tens digits is 10.
The two numbers can be?
:
1st two digit number 10a + b
2nd two digit number 10c + d
:
"The product of two two-digit numbers is 1484."
(10a + b)&(10c + d) = 1484
FOIL
100ac + 10ad + 10bc + bd
:
"The product of their units digits is 24"
b * d = 24
:
"the product of their tens digits is 10."
a * c = 10
We know that a is 5 and c is 2 or vice versa
:
In the 1st equation, we find we can replace bd with 24 and ac with 10
100(10) + 10ad + 10bc + 24 = 1484
1000 + 10ad + 10bc + 24 = 1484
10ad + 10bc + 1024 = 1484
10ad + 10bc = 1484 - 1024
10ad + 10bc = 460
Simplify, divide by 2
5ad + 5bc = 230
:
Assume a=2, c=5
2(5d) + 5(5b) = 230
10d + 25b = 230
10d = 230 - 25b
d = 23 - 2.5b
Only two single digit integer solutions to this equation:
b=8; d=3 (the only pair that satisfy eq: b * d = 24)
and assuming; a=2; c=5
therefore:
28, 53 can be the numbers
:
check: 28 * 53 = 1484
