Questions on Word Problems: Coins answered by real tutors!

Sam has $3.15 in quarters nickels and dimes he has half as many quarters as he has dimes and nickels together he also has two more nickels than dimes how many of each coin are there

Appears as though this should be written as:
"Sam has $3.15 in quarters, nickels, and dimes. He has half as many quarters as he has dimes and nickels, together. 
 He also has two more nickels than dimes. How many of each coin are there?"

Let number of dimes be D
Then number of nickels is D + 2 (He has 2 more nickels than dimes)
Number of quarters:  (He has half as many quarters
                                                         as he has dimes and nickels, together)
Amount in DIMES: .1D
Amount in NICKELS:  .05(D + 2) = .05D + .1
Amount in QUARTERS: .25(D + 1) = .25D + .25 
Total amount: $3.15 
We then get: .1D + .05D + .1 + .25D + .25 = 3.15
                                .4D + .35 = 3.15
                                      .4D = 2.8
                   Number of dimes, or 

                 Number of nickels: D + 2 = 7 + 2 = 9
                Number of quarters: D + 1 = 7 + 1 = 8

In fact, you can even use artificial intelligence.  You cannot trust AI for
advanced stuff, but it can solve simple stuff very easily.  I copied and pasted
exactly word-for word what you posted above (without punctuation marks) into: 

https://poe.com/

and here's what I got (copied and pasted) from that site:

-------------------------------------

Let's define the variables for the coins:

Let 𝑑 be the number of dimes.
Let 𝑛 be the number of nickels.
Let 𝑞 be the number of quarters.

From the problem, we have the following relationships:

The total value of the coins is $3.15, which is 315 cents:

10𝑑+5𝑛+25𝑞=315

Sam has half as many quarters as the total number of dimes and nickels:
𝑞=1/2(𝑑+𝑛)

He has two more nickels than dimes:
𝑛=𝑑+2

Now, we can substitute 𝑛 in terms of 𝑑 into the other equations. 

From the third equation, we have: 𝑛=𝑑+2

Substituting 𝑛 into the second equation:
𝑞=(1/2)(𝑑+(𝑑+2))=(1/2)(2d+2)=d+1

Now substituting 𝑛 and 𝑞 into the first equation:

10𝑑+5(𝑑+2)+25(𝑑+1)=315

Expanding this gives:

10𝑑+5𝑑+10+25𝑑+25=315

40𝑑+35=315

Now, subtract 35 from both sides:

40𝑑=280

Dividing by 40:

𝑑=7

Now that we have d, we can find 𝑛 and 𝑞
𝑛=𝑑+2=7+2=9
𝑞=𝑑+1=7+1=8

Thus, the solution is:

Dimes (d): 7
Nickels (𝑛): 9
Quarters (𝑞): 8
Final Answer:

Dimes: 7
Nickels: 9
Quarters: 8

-------------------------

That was all copied and pasted exactly as poe.com printed instantly. But
don't depend on it for more advanced math.  It will sometimes make stupid
mistakes.  AI is not perfected yet.  But someday it will be, and will take us
all over, just as Stephen Hawking warned. LOL (Maybe I shouldn't be laughing).

Edwin

Apparently the younger generation doesn't see any need for punctuation marks or
capital letters to separate sentences.  They just run them all together. And
soon the correct way to write will include "u" for "you", "r" for "are",
"before" as "b4", "8" for "ate", etc.  

In that light, there are plenty of sites online where you only have to type in a
system of equations, point and click, and the answer pops out instantaneously.
So why not use them?   You can even do it on a TI-84 calculator, if you install
the right program.  Why hitch a horse to a buggy and get there in an hour, when
you can drive a car and get there in 10 minutes? 

If you use a separate letter for each unknown, setting up the equations is a
cinch. This system below is set up directly from the words:



Go to one of those sites. Type that in. Point and click, and instantly you 
get q=8, d=7, n=9.  Here is a link to such a site:

https://www.emathhelp.net/en/calculators/algebra-2/system-of-equations-solver/?

Edwin