coin and interest math problem help

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white92
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coin and interest math problem help

Postby white92 » Wed Dec 17, 2008 5:26 pm

I've been sick and away from school and my teacher sent me 4 problems and I can't figure them out. If someone could help me figure this one problem out, then maybe I could figure out the rest. Okay, here is the problem-

Sarah is overwhelmed with Christmas spirit and has given Santa's helper, Mini-me, the entire contents of her wallet. Mini-me is quite happy now because he has twice as many twenty-dollar bills as he does one dollar bills, and three more ten dollar bills as he does one-dollar bills for a total of $285. How many twenty, tens, and ones does Mini-me have?

Thanks a lot!

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stapel_eliz
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Postby stapel_eliz » Wed Dec 17, 2008 6:17 pm

I've been sick and away from school and my teacher sent me 4 problems and I can't figure them out.
It can be hard to try to work just from the book and whatever class notes your friends have sent home. :shock:

To learn some of the general background material, try here:

. . . . .Translating Word Problems

. . . . .Solving Linear Equations

. . . . ."Coin" Word Problems

That last one is really about "money" problems; most such are stated in terms of coins, rather than bills, but the concepts and methods are exactly the same. :wink:
Mini-me...has twice as many twenty-dollar bills as he does one dollar bills, and three more ten dollar bills as he does one-dollar bills for a total of $285. How many twenty, tens, and ones does Mini-me have?
You'll probably "see" how to do this as soon as you've worked through a couple examples in the "coin" lesson above, but the general set-up is as follows:

. . .numbers of bills:
. . . . .$1: x
. . . . .$20: 2x
. . . . .$10: ??

. . .value of bills:
. . . . .$1: (1)(x) = x
. . . . .$20: (20)(2x) = ??
. . . . .$10: ??

Complete the table. Add up the values of each type of bill, and set this equal to the given total. Then solve for the variable, and back-solve for the requested values.

If you get stuck, please reply with a clear listing of your work and reasoning so far. Thank you! :D

Eliz.

white92
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Re: coin and interest math problem help

Postby white92 » Wed Dec 17, 2008 11:21 pm

Okay, I got stuck. I appreciate your help btw. :)

$20=2x
$10=3x
$1=x

Then I did

(20)(2x)+(10)(3x)+(1x)

30+6x=285

I subtracted 30 from both places and got

6x=255

divided 6 by 255 but then came up with 42.5 so I did something wrong, I guess.
Is the 1x supposed to be just x alone? so instead of adding all of the x's and coming out with 6x, I'd come out with 5x?

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stapel_eliz
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Postby stapel_eliz » Wed Dec 17, 2008 11:52 pm

$20=2x
$10=3x
$1=x
According to your "translation" above, the exercise actually stated that there were "three times as many" tens as ones, rather than "three more" tens than ones. Is that correct?
(20)(2x)+(10)(3x)+(1x)

30+6x=285
How did you arrive at "30 + 6x" from "40x + 30x + 1x"?

. . . . .Simplifying with Parentheses

Please reply with the steps between your two quoted lines above. Thank you! :D

Eliz.

DAiv
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Re:

Postby DAiv » Thu Dec 18, 2008 1:45 am

(20)(2x)+(10)(3x)+(1x)

30+6x=285
How did you arrive at "30 + 6x" from "40x + 30x + 1x"?

. . . . .Simplifying with Parentheses

Please reply with the steps between your two quoted lines above. Thank you! :D

Eliz.
I hope I'm not stepping on any toes, but I think I can see what has happened.

No multiplication has been done at all. All non-x-values have been summed (20 + 10) = 30, as have all x-values (2x + 3x + 1x) = 6x.

This would lead me to believe that white92 has yet to learn that the values in adjacent parentheses (side-by-side)(round brackets) must be multiplied, rather than all like terms added together.

Perhaps showing how this part of the equation is said out loud would help:

"(20)(2x)+(10)(3x)+(1x)" is pronounced "Twenty times two ecks, plus ten times three ecks, plus one ecks"

DAiv


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