10

Wed 3 Mar, 2010 02:03 pm
Two whole numbers are each between 50 and 70.

They multiply to make 4095.

What are the missing numbers?

_______ X _________ = 4095

(my daughter's maths homework, we cannot figure it out!)

many thanks.
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Type: Question • Score: 10 • Views: 15,420 • Replies: 33
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rosborne979

1
Wed 3 Mar, 2010 02:23 pm
@Dorothy Parker,
63 and 65 will do it, but I have no idea how to figure it out mathematically.

Since the result ends in a 5, one of the multipliers must end in a 5, but other than that I don't know how to find the answer mathematically.
0 Replies

aidan

2
Wed 3 Mar, 2010 02:26 pm
@Dorothy Parker,
Well, you know that at least one of the multipliers has to have a 5 in the one's place because your product is a multiple of 5. So one of your multipliers has to be either 55 or 65 because those are the only two whole numbers that fit the criteria between 50 and 70. So I divided 4095 by 65 and got 63.

65x63= 4095
Francis

1
Wed 3 Mar, 2010 02:31 pm
Well, let's see:

I order for the result to end with 5 (4095), one of the numbers you are looking for needs to end with 5.

What are the numbers between 50 and 70 that end with 5?

Only 55 and 65 fit the requirement.

The other one needs to end with 1 or 3 or 5 or 7 or 9.
so the list is: 51 53 55 57 59 61 63 65 67 69.

It will not take long for you to find out when multiplying one of the former by one of the latter..
Dorothy Parker

1
Wed 3 Mar, 2010 02:41 pm
Thank you so much for speedy replies guys.

0 Replies

JPB

1
Wed 3 Mar, 2010 03:39 pm
@aidan,
right, and the only other thing you need to check is that 55 doesn't work. 4095/55 = 74.45 which is not a whole number and not between 60 and 70.
aidan

1
Wed 3 Mar, 2010 03:50 pm
@JPB,
I knew 55 wouldn't work because there's no number lower than 70 by which you could multiply 55 that would give you a product as high as 4,095 (or even 4,000 which is what I rounded it off to in my head when I was thinking about which of the two possible options made more sense).
JPB

1
Wed 3 Mar, 2010 03:53 pm
@aidan,
good, but that doesn't mean that dp's daughter would know that intuitively.
aidan

1
Wed 3 Mar, 2010 04:15 pm
@JPB,
Quote:
good, but that doesn't mean that dp's daughter would know that intuitively.

Could be - although if she's in fourth or fifth grade, she may have been taught how to estimate, and that's one of the important steps in considering possibilities for solving a problem such as this. But you're right - she may not have known how or to do that intuitively. I was just explaining why I chose to divide by 65 instead of 55. Maybe she'll read that or DP will explain it to her- that sort of logic will help her with problems like these in the future.
0 Replies

oolongteasup

1
Thu 4 Mar, 2010 03:37 am
@Dorothy Parker,
i suspect the answer is untenable
0 Replies

Dorothy Parker

1
Mon 8 Mar, 2010 02:07 pm
Unfortunately, I am unable to explain the working out of this maths problem. Even if I were to re-read it a hundred times, I would still not understand it. I have never been any good at maths. It used to reduce me to tears at school cos I just could not get my head round certain things.

God knows how I will help her with the maths homework when she's at high school.
georgeob1

1
Mon 8 Mar, 2010 02:15 pm
@Dorothy Parker,
The square root of 4095 is 63.992. The square of 65 is 4225.

So you're looking for two numbers near 65 whose product ends in 5.

63 times 65 comes quickly to mind, and that is the answer.
Dorothy Parker

1
Mon 8 Mar, 2010 02:16 pm
@georgeob1,
ok :-)
0 Replies

Francis

1
Mon 8 Mar, 2010 02:17 pm
@georgeob1,
However, dear George, it doesn't solve DP's main problem..
OCCOM BILL

1
Mon 8 Mar, 2010 02:17 pm
@Francis,
Francis wrote:

Well, let's see:

I order for the result to end with 5 (4095), one of the numbers you are looking for needs to end with 5.

What are the numbers between 50 and 70 that end with 5?

Only 55 and 65 fit the requirement.

The other one needs to end with 1 or 3 or 5 or 7 or 9.
so the list is: 51 53 55 57 59 61 63 65 67 69.

It will not take long for you to find out when multiplying one of the former by one of the latter..
Show this post to your daughter. She'll probably understand it just fine.
Francis

1
Mon 8 Mar, 2010 02:20 pm
@OCCOM BILL,
You have a point, Bill.

People I used to teach, were usually older than DP's daughter..
0 Replies

georgeob1

1
Mon 8 Mar, 2010 03:42 pm
@Francis,
Yes it does. I merely ommited the tedious detail, which in your Gallic (almost Germanic) thoroughness, you insisted on including. My explanation hit all of the essential ideas.
Francis

1
Mon 8 Mar, 2010 03:53 pm
@georgeob1,
It seems to me that DP's problem is how to explain that to her daughter.

If your explanation is understandable to a seven or eight years old, I'm probably missing something..
McTag

1
Mon 8 Mar, 2010 04:41 pm
@aidan,

Quote:
Well, you know that at least one of the multipliers has to have a 5 in the one's place because your product is a multiple of 5. So one of your multipliers has to be either 55 or 65 because those are the only two whole numbers that fit the criteria between 50 and 70. So I divided 4095 by 65 and got 63.

65x63= 4095

georgeob1

1
Tue 9 Mar, 2010 12:18 am
@McTag,
On reflection, I prefer Aidan's as well.

Mine is second best. I forgot about the 50 & 70 limits and just looked for numbers close to 65. However didn't have the inspired insight to divide by 65.

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