Question

I don't understand this please help...
A collection of dimes and nickels is worth $6.90. There are 96 coins in all.

How many of each coin are there?

dimes
nickels

Answer 1

welcome to open study

Answer 2

Hai

Answer 3

You need to set up 2 equations here

Answer 4

Total Coins = Dimes + Nickles

Let D = # Dimes and N = # Nickles

96 = D + N

Answer 5

0.10x + 0.05y=6.90

x+y=96

Answer 6

right those are the ones

Answer 7

but what do I do now ?

Answer 8

Need to find the value for X and Y that will make both of those equations true, there are a couple different ways to go about that

Answer 9

We will do a substitution here....Solve one equation for X first

X + Y = 96
so
X = 96 - Y

Answer 10

good?

Answer 11

Mhm

Answer 12

Now, replace X in the other equation by X = 96 - Y

0.10x + 0.05y = 6.90

0.10*(96-y) + 0.05y = 6.90

Answer 13

that make sense there?

Answer 14

That would make 9.60-0.10y+0.05=6.90

Answer 15

yes, just forgot the y after 0.05

Answer 16

Oh yeah, sorry

Answer 17

Combine like terms ?

Answer 18

9.60- 0.10y+ 0.05y = 6.90

add together the y's

9.60 - 0.05y = 6.90

subtract 9.60

-0.05y = -2.70

Divide by -0.05

y = 54

Answer 19

y here is the number of nickles

# nickles = y = 54

Answer 20

nickles=54 and dimes=42? Correct ?

Answer 21

You can test it,

Total coins = 96 = 54 + 42 ?

6.90 = 0.05*54 + 0.10*42 ??

if both are true, then you have the right answer

Answer 22

Thanks A lot =D

Answer 23

welcome, anytime