Question

AWARD AND MEDALLLLL
Your piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have?

Answer 1

You need some variables here. Let D=# of dimes, and Q=# of quarters. Can you write an equation to model the fact that the total number of coins is 46?

Answer 2

D+Q=46

Answer 3

Good! Now we have 2 variables, so we need 2 equations. How about an equation that models the fact that the total value of the coins is 7.00?

Answer 4

D(.10)+Q(.25)=7.00

Answer 5

Excellent! Now, you probably don't like those pesky decimals in that equation any more than I do, do you? I would probably eliminate the decimals in that 2nd equation. How can we do that?

Answer 6

And what do you get when you do?

Answer 7

uhm, multiply each number by 100. D(10)+Q(25)=700

Answer 8

Look at you go! You hardly need my help. :) Yes, what that did is basically converted that 2nd equation from being in terms of dollars to being in terms of cents.

Now you have these 2 equations.

D+Q=46
10D+25Q=700

2 equations.... 2 unknowns.... do you know what to do from here? That first one is conveniently easy to solve for either variable, and then plug into the 2nd equation.

Answer 9

ooops nevrmind

Answer 10

hmmm.... I don't think so, how did you get to that point? Did you solve the first equation for one of the variables? (I suggest solving for D in terms of Q, but either way will work)

Answer 11

I'm kind of stuck :| Sorry

Answer 12

That's ok, let's take it apart a little bit now. You have these 2 equations:

D+Q=46
10D+25Q=700

Let's solve that first one for D. In other words, shuffle the equation around so you have D=?

Answer 13

D=46-Q

Answer 14

Good. That's "D in terms of Q" because it expresses D based on what Q is. Now you can take THAT expression for D, and plug it into the OTHER equation where you see D.

10(D)+25Q=700
Replace the D with (46-Q)

Answer 15

That will give you an equation in ONE variable. Just simplify the expressions and isolate the variable Q, and you will get a value for Q.

Once you have that value for Q, you can plug THAT back into your equation that gives D in terms of Q, and you will get D.

And then of course, you can CHECK your answer, making sure it fits what the original problem said. :)

Answer 16

10(46-Q)+25Q=700
460-10Q+25Q=700
460-35Q=700
700-460=240
35Q=240
I come up with a weird/ long decimal....What did I do wrong?

Answer 17

What is -10Q+25Q? :)

Answer 18

ooh I forgot that it was negative

Answer 19

That will make a big difference. :)

Answer 20

10(46-Q)+25Q=700
460-10Q+25Q=700
460-15Q=700
700-460=240
240/15= 16
Q=16

Answer 21

Great! Now you know Q, so how do you get D?

Answer 22

Subtract 240 from 700 and divide it by 10

Answer 23

Wait thats not right

Answer 24

haha... nooo.... you are making it too hard. You KNOW Q. You want D. Do you have an equation at your fingertips that... oh, I don't know.... give you D in terms of what Q is? Hm??

Answer 25

(up approximately 11 posts) :)

Answer 26

You ok? Figure it out?

Answer 27

Oops sorry

Answer 28

there are 16 quarters and 10 dimes

Answer 29

How did you get 10 for the dimes?

And does that add up to the amount of money that there is supposed to be?

Answer 30

You have an equation for dimes, given quarters:

D-46-Q

So since you know quarters, that equation will let you figure the dimes.

Then the total coins should add to ----- how many?
And the total value of the coins should be ---- how much?
Neither of these ^^^ checks will work with 16 quarters and 10 dimes.