Question

Eleanor has $1.60 in nickels and dimes. If there are 3 times as many quarters as nickles, how many of each type of coin does she have?

Answer 1

We just need help with this one question so we can figure out the rest of the sheet.

Answer 2

quarters?

Answer 3

Yes.
Like in money.

Answer 4

Note:
a "quarter" is a quarter dollar, worth $0.25
a "nickel" is a 5 cents coin, worth $0.05.

Solving mentally:
If there are three times as many quarters as nickels, then for every 3 quarters, we get a nickel for a sum of 3*0.25+0.05=$0.80.
So $1.60 will have 2 sets of the above, or 6 quarters, and 2 nickels.

Solving algebraically:
Let N=number of nickels (each =0.05$) =>
3N = number of quarters (each worth 0.25$).
So
3N*0.25+N*0.05=1.60
0.80N = 1.60
N=1.60/0.80=2 (number of nickels)
3N = 3*2=6 = number of quarters).
So answer: 6 quarters and 2 nickels for a total of $1.60.

Answer 5

Okay, thank you very much for explaining! ^^ This should help as a example for the rest of the sheet.

Answer 6

Good, just post if you have difficulties.

Answer 7

Okay, we will! Thanks again!

Answer 8

It says "Eleanor has $1.60 in nickels and dimes" though.

Answer 9

Oooh, I just read that there are "nickels and dimes", and later it says there are nickels and quarters. I think it's quarters, because dimes don't make an integer solution. Please check for typo.

Answer 10

It's quarters sorry, we just saw the typo!
We're very sorry you guys! D:

Answer 11

No problem!

Answer 12

Solve the following for q, n and d:\[\left\{5n+10d=160,\frac{q}{n}=3\right\}\]\[\left\{n\to \frac{q}{3},d\to 16-\frac{q}{6}\right\} \]q has to be divisible by 6. Replace q by 6. Then:\[\{n\to 2,d\to 15\} \]5*2 + 10*15 = 160 ?
10 + 150 = 160
0.10 + 1.50 = 1.60