Question

I feel stupid for not knowing this.......

Answer 1

i generally feel stupid regardless of whether or not i know anything :)

Answer 2

@@

Answer 3

Tom had some stamps. If he gave 7 stamps to each of his children he would have 5 stamps left. If he gave 8 stamps to each of his children , he would need 3 more stamps in order for the children to have an equal number of stamps. How many stamps did Tom have ?

I started with :
x = total number of stamps
y = number of children

x - 7y = 5
but I can't figure the second equation....
I tried x - 8y = -3, but that doesn't work.

I just need the second equation

Answer 4

x - 8y = x + 3 ???

Answer 5

oh...the 1st equation is wrong ?

Answer 6

s - 7c = 5
8c + 3 = s

maybe

Answer 7

no i was wrong, sorry
i thought it was a divisibility problem

Answer 8

This is actually trickier than I thought it would be when I read it. We somehow need to represent the remainder of x/y as 3? So maybe x/y = c+ 3/y where c is some whole number?

Answer 9

wouldn't that be the same as x - 7y = 3

Answer 10

8c + 3 - 7c = 5

c = 2

19 = s

19 - 7(2) = 5
8(2) + 3 = 19

is what im thinking

Answer 11

but that "to have an equal number of stamps" seems odd to me

Answer 12

that seems to work.....wow, only 2 kids....I was expecting more...lol

Answer 13

okay....thanks....19 stamps in total

Answer 14

I was trying to work on two equations when only one was needed.....I feel stupid

Answer 15

im not sure its absolutely correct tho :) if he has 2 children and 19 stamps, then 9 stamps each leaves 1 stamp left over ..... but that doesnt really obfuscate the situation

Answer 16

but when you checked it.....it seems to equal

Answer 17

when i check it it works fine ... but im wondering if that "needs 3 more" plays into it or not.

if he has 19 stamps and 2 kids; then after 8 per kid he would still need 3 more to even it out, but if its meant to portray an actual need of 3, as opposed to giving the kids 9 stamps and needing just 1 ... i cant say

Answer 18

I see what you are saying....he could have given 9 stamps and having 1 left.....I am just going to put 19.

Answer 19

im getting stamps = 53

Answer 20

How many kids you getting ?

Answer 21

let me verify again

Answer 22

x be the # of kids,
then

7x leaves 5
8x leaves 5

Answer 23

x = 7y + 5 -->
x + 3 = 8y

7y + 5 + 3 = 8y
8 = y

x + 3 = 8y
x + 3 = 8(8)
x = 64 - 3
x = 61

oh....could it be 8 kids and 61 stamps ?

Answer 24

13 kids

Answer 25

I wish this was multiple choice...it would be so much easier

Answer 26

spose he has 4 kids, just a random number

7(4) = 28 + 5 = 33 stamps

8(4)= 32 + 1 left over, and he needs 3 more stamps to even it out

Answer 27

oh....that would even it out

Answer 28

stamps is looking tricky

Answer 29

but, does the question imply that 5 stamps left over does not spread evenly over the kids?

Answer 30

the question is ill formed and can relate to multiple interpretations

Answer 31

lol.....I don't feel so stupid now

Answer 32

lol

Answer 33

I was trying to help my sister with this problem.....now, I don't know if I can....it is confusing.....and she is in 6th grade

Answer 34

thank you guys for your help :)

Answer 35

if we have 8 children :) just becasue 5+3 = 8

7(8) + 5 = 61

8(8) = 64 , which is 61+3 to even it out

Answer 36

so simple it was !

Answer 37

(7x+5) + 3 = 8x

Answer 38

thanks amistre :)

Answer 39

:) your welcome

Answer 40

great.....8 kids and 61 stamps......thanks so much

Answer 41

it was easy but somehow i took so much time lol

Answer 42

I know.......I didn't even start it right...I was trying to work with 2 equations

Answer 43

i feel happy having a company :)

Answer 44

having a company ?

Answer 45

I am curious to what whpalmer is going to say

Answer 46

"Tom had some stamps. If he gave 7 stamps to each of his children he would have 5 stamps left. If he gave 8 stamps to each of his children , he would need 3 more stamps in order for the children to have an equal number of stamps. How many stamps did Tom have ?"

Tom starts out with some quantity of stamps. He gives out 7 each to his kids, and is left with 5. That part seems pretty clear. For any number of kids, \(k\), he needs \(7k+5\) stamps to be able to distribute 7 to each kid and have 5 left.

The second part could perhaps be more clearly written as "he needs 3 more stamps than he currently has to be able to give 8 stamps to each of his children."
The number of stamps here is \(8k-3\)

The numbers of stamps are identical due to the well-known principle of word problem stamp conservation(*) — no stamps enter or leave the problem, so the quantity is unchanged. That gives us \[7k+5 = 8k-3\]\[7k+8 = 8k\]\[ k = 8\]\(8\) kids and \(7(8)+5 = 61\) stamps.

(*) You hadn't heard of it? Shocking! :-)

What is moderately interesting, and possibly a pitfall for someone trying to solve this by brute-force without sufficient consideration, is that you can get apparent solutions if you forget to specify that the number of kids must be the same. One might think you could solve this similarly to computing the LCM of some numbers by just making a list of numbers and looking for the first match:

7 stamps per kid: 5 12 19 26 33 40 47 54
8 stamps per kid: -3 5 13 21 29 37 45 53

Hey, look at that, both lists have 5! That must be a solution...er, wait, there aren't any kids. And later on in the lists, you'll have numbers such as 117 which appear in both lists, but as a different term, which is also true of 5, but we ruled that out when we noticed there were 0 kids in the 7 stamps per kid case, and probably didn't even look at the 8 stamps per kid case to notice that was with 1 kid, not 0.

Answer 47

I did the exact same thing, u can make out that easily by my replies above lol i feel stupid

Answer 48

lol.....he makes it sound so easy, which it really is.....I didn't catch on right away

Answer 49

thanks whpalmer :)

Answer 50

I will close this now.....you guys and girls are lifesavers :)

Answer 51

Here's a list of the numbers in two columns, one for 7, one for 8, up to the world record of 69 kids by a single mother :-) More than a few "matches" between the columns, but only the one with the same number of kids. If you think of this as two lines (s = 7k+5, s = 8k-3) it's clear there can only be one intersection. Fortunately it ends up being at an integral number of kids, so we don't need to invoke King Solomon :-)



Grid[Table[{kids*7 + 5, kids*8 - 3}, {kids, 0, 69}]]
{
{5, -3},
{12, 5},
{19, 13},
{26, 21},
{33, 29},
{40, 37},
{47, 45},
{54, 53},
{61, 61},
{68, 69},
{75, 77},
{82, 85},
{89, 93},
{96, 101},
{103, 109},
{110, 117},
{117, 125},
{124, 133},
{131, 141},
{138, 149},
{145, 157},
{152, 165},
{159, 173},
{166, 181},
{173, 189},
{180, 197},
{187, 205},
{194, 213},
{201, 221},
{208, 229},
{215, 237},
{222, 245},
{229, 253},
{236, 261},
{243, 269},
{250, 277},
{257, 285},
{264, 293},
{271, 301},
{278, 309},
{285, 317},
{292, 325},
{299, 333},
{306, 341},
{313, 349},
{320, 357},
{327, 365},
{334, 373},
{341, 381},
{348, 389},
{355, 397},
{362, 405},
{369, 413},
{376, 421},
{383, 429},
{390, 437},
{397, 445},
{404, 453},
{411, 461},
{418, 469},
{425, 477},
{432, 485},
{439, 493},
{446, 501},
{453, 509},
{460, 517},
{467, 525},
{474, 533},
{481, 541},
{488, 549}
}

Answer 52

your a busy man to figure all of this.......math whiz

Answer 53

Oh, it was just a few seconds to type a command or two, and then copy/paste. Many more seconds to think of a coherent way to explain it :-)

Answer 54

you could be one of those people to solve one of the math questions that no body has ever solved...the ones where you can make a ton of money to solve.

Answer 55

nobody gets money solving math questions though, oly personal selfish pleasure one gets which is worth billions of dollars :)

Answer 56

I suppose your right.....