Question

A coin collection jar is full of just nickels and dimes. If there are 355 coins valued at $24.45, how many nickels are in the jar?

Answer 1

two equations: # of nickels + # of dimes = 355
# of nickels * 0.05 + # of dimes * 0.10 = 24.45

solve the system and you'll have your answer

Answer 2

the important thing is that you have 24.45 dollar. that's all matter :D

Answer 3

do you know how to solve such a system of equations?

Answer 4

Yes, give me a minute, I was trying to figure it out and didn't realize I got a reply on here.

Answer 5

I'm stuck..

Answer 6

What are you stuck on?

Answer 7

what do you have for the equations?

Answer 8

I don't understand the equation that was given up there^

Answer 9

isn't there supposed to be variables?

Answer 10

Lets let nickels be "n" and Dimes be "d"

We know there are some amount of both that add to 355 coins...

Now we also know that each nickel is .05 and each dime is .10...this adds up to 24.45

so

n + d = 355
.05n + .10d = 24.45

how's that look?

Answer 11

well, I gave them in words: "# of dimes" could be d, # of nickels could be n

Answer 12

okay yeah i wrote down 0.05n+0.10d=24.25?

Answer 13

now i solve for n?

Answer 14

not quite: 24.45!

Answer 15

well 24.45 but yeah

Answer 16

oh, typo lol :)

Answer 17

typo which will destroy any chance at a correct answer...

Answer 18

lol! okay I got:

n=24.45-0.10d/0.05?

Answer 19

here's how I would do it:

n + d = 355
0.05n + 0.10d = 24.45

multiply the second equation by 100 to clear out the pesky decimals

n+d = 355
5n + 10d = 2445

(alternatively, think of the problem in cents instead of dollars)

now solve the first equation for either n or d, and plug that in the second one

Answer 20

giving you an equation in just one variable which is easily solved. then use the first equation to get the value of the other variable

Answer 21

wait, first equation as in n+d=355?

Answer 22

n=355-d

Answer 23

Right...so now substitute that into your second equation for 'n'

Answer 24

355-n=2445-10d/5 and solve for d?

Answer 25

5n + 10d = 2445

after plugging in n = 355 - d

5(355 - d) + 10d = 2445

and simplify from here...do you see what I did there? simply replaced 'n' with what 'n' equals (355 - d)

Answer 26

ohhh, ahh i did it wrong again. hold on

Answer 27

d=134 n=221?

Answer 28

That is what I got!

Answer 29

i plugged the amount of dimes back into 5n+10d=2445 right?

Answer 30

Yeah recheck your answer....plug both those numbers back in and see if you get 2445

Answer 31

Yes sir, 5(221)+10(134)=2445

Answer 32

So then we have the correct answer :)

Answer 33

Thank you :) I'm horrible with word problems lol

Answer 34

Thank you to you to @whpalmer4 :)

Answer 35

in general, you need to check your solution in all of the equations of the system: it's possible to come up with "solutions" that work for only some of the equations, not all.

for example, 240 dimes and 9 nickels would give you $24.45, but fail the 355 coins equation

Answer 36

wait thats wrong ;/ it says 225 is nickels

Answer 37

and its wrong by my mistake, dang it! it's $24.25 in the book.

Answer 38

oh lordy, let me see if i can fix it though and get the right answer

Answer 39

Ahh...well yes if it is 24.25 in the book then yes 225 would be correct...but yeah lol

Answer 40

okay got it! d=130 and nickels=225

Answer 41

=2425

Answer 42

I'm going to give you two more ways you could solve this:

1-variable approach:

if there are 355 coins, we can say that x is the number of nickels, and 355-x is the number of dimes, right? we could write just one equation:

5x + 10(355-x) = 2425 (I'm doing it in cents to skip the multiply by 100 step)

5x + 3550 - 10x = 2425
3550 - 5x = 2425
3550-2425 = 5x
1125 = 5x
225 = x

so 225 nickels, 355-225 = 130 dimes


in your head approach:
assume all of the coins are dimes: 355 dimes = $35.50. that's too high by $35.50-$24.25 = $11.25. each dime we change to a nickel reduce the amount by $0.05. We need $11.25/$0.05 = 225 nickels instead of dimes.

Answer 43

if you have an easy way of making graphs, graphing the lines n+d=355 and 5n+10d=2425 and finding the point where they intersect also gives you the solution.

Answer 44

thank you :)

Answer 45

it turns out that most word problems you commonly encounter fall into a couple of different categories, and once you figure out to solve the problems in each category, you're in good shape. there is a good book by Rebecca Wingard-Nelson that you can probably find at the library and become a wizard at doing these :-)