coin and interest math problem help

[white92]

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!

[stapel_eliz]

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.

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.

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!

Eliz.

[white92]

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?

[stapel_eliz]

$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!

Eliz.

[DAiv]

(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!

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