Question

A collection of nickels, dimes, and quarters totals $8.20. The number of nickels and dimes
together is twice the number of quarters. The value of the nickels is one-third the value of the
dimes. How many of each kind of coin are there?

Answer 1

Assume you have n nickels, d dimes, and q quarters. You know that the number of nickels and dimes together is equal to two times the number of quarters. Can you write that in a mathematical equation?

Answer 2

so is that .25(1/2( d+n)?

Answer 3

Not quite. A lot of the trick with word problems is interpreting the words into mathematical expressions.
"the number of nickels and dimes together is equal to two times the number of quarters"
n + d = 2 times q\[n + d =2q\] Now can you do that with these words?
The value of the nickels is one-third the value of the dimes.

Answer 4

d/3

Answer 5

n=d/3

Answer 6

The trick here is you are comparing the value of the nickels to the values of the dimes, not the number.
0.05 n = total value of the nickels
so
\[0.05n=\left( 0.10d \over 3 \right)\]

Answer 7

So now you have two of the three equations you need. The final equation we can get from the statement: the collection of nickels, dimes, and quarters totals $8.20. Hint: we are dealing with the value again. What do you think this equation would be?

Answer 8

so... \[.10d+.10d/3+ .25(1/2(10d/3 +d)=8.20\]

Answer 9

is this right?

Answer 10

What answer did you get for d?

Answer 11

Well, just FYI. I got 24 dimes.

Answer 12

was this the right equation

Answer 13

Let n, d and q be the number of nickels, dimes and quarters respectively.
Solve the following equations for n, d and q:\[\left\{5n+10d+25q==820,n+d==2q,\frac{10d}{5n}==3\right\} \]\[\{n=16,d=24,q=20\} \]