What would the equation(s) be??

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synapsis

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I can't write an equation for this problem, my nephew was having a problem with his homework and so i got a call. It turns out that an A in college algebra isn't enough. It's got to be simple i just can't figure it out.

There are 3 times as many dimes as nickles.
There are 4 more quarters than nickles.
The total of the coins is 9.40.
How many of each coin?
 
>There are 3 times as many dimes as nickles.
There are 4 more quarters than nickles.
The total of the coins is 9.40.
How many of each coin?

Realize that there is a difference between the number of coins and their value.
You have got to name things and write it down.
If you let d be the number of dimes, then 10d represents the value of d dimes.
If you let n be the number of nickels, then 5n represents the value of n nickels.

Now, can you write two equations in two unknowns and solve simultaneously?
 
Thanks, but that still doesn't answer my question what the formula looks like, or maybe i'm overthinking this that there is a formula. Wouldn't it actually be .1D and .05N and .25Q? Process and elimination could get me the answer but i figure there is a more logical way by way of an equation.
 
synapsis said:
Wouldn't it actually be .1D and .05N and .25Q?
Click to expand...
If you work in "dollars" instead of "cents", yes, one would use your expressions. But the answer will work out the same, either way.

To learn the general method, try studying this lesson on "coin" exercises. Then translate the English statements into mathematical expressions and equations.

Since the numbers of dimes and quarters are expressed in terms of their relationship to the number of nickels, pick a variable for the number of nickels; "n" would be useful.

Write an expression, in terms of this variable, for the number of dimes.

Write another expression, in terms of the same variable, for the number of quarters.

Then following the reasoning displayed in the previous reply (and in the online lesson) to express the values of those numbers of coins. For instance, since each nickel is worth five cents (or 0.05 of a dollar), then the value of "n" nickels is given by 5n (or by 0.05n).

Sum the value expressions, and set equal to the given total of 940 cents (or 9.4 dollars). Solve the equation for the value of the variable. Then back-solve, using the expressions for the numbers of dimes and quarters, to find the answer.

If you get stuck, please reply showing how far you have gotten. Thank you! :D
 
Sorry. I misled you because I didn't read your problem thoroughly. I see you have a response from Stapel which is probably the best way to attack the problem. You will end up with the value of the nickels + value of dimes in terms of nickels + value of quarters in terms of nickels = total value of coins.
 
I overthought this- here is what i got i gues i solved my nephews problem...

(.25N +1) + (.05N) + (.3N) = 9.40
.6N +1 = 9.40
.6N = 8.40
14 = N

Plug in N for

Quarters= N+4= 18 quarters...
Nickles= N = 14 nickles...
Dimes= 3N = 42 dimes...

Pretty simple

Thx for your help
 
Well ok...but not "clear"...
Variable(s) must be "declared"; teachers would expect a solution a bit like:

Let n = number of nickels
Then number of dimes = 3n, number of quarters = n + 4

.05(n) + .10(3n) + .25(n + 4) = 9.40 ; next step could be multiplication by 10 (get rid of decimals):
5n + 10(3n) + 25(n + 4) = 940
5n + 30n + 25n + 100 = 940 ... leads to n = 14

Just a suggestion.
 
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