A collection of nickels and dimes is worth $9.45 if the number of dimes is doubled the value is $16.65 find the number of each coin

Answer 1

x = Number of nickels

y = Number of dimes 0.05 x + 19.90 - 0.10 x =16.65

two unknowns need two equations

0.05 x - 0.10 x = 9.45

0.05 x + 0.10 (2y) =16.65

Solve for y in first equation: (9.45 - 0.05x) / 0.10 = y

Substitute the value for y in the second equation: 0.05 x + 0.10 ( 2 ( ( 9.45 - 0.05 x) / 0.10) = 16.65

x = 45 coins

Solve for yin first equation: (9.45 - 0.05(45))/10 = y

y = 72 coins

Verify: 0.05 (45) + 0.10 (72) = 9.45

2nd equation : 0.05 (45) + 0.10 (72) = 16.65

Answer 2

Hello!

so set the nickels (n) and dimes (d) equal to 9.45. However, you also need to account for the fact that you are solving for money, not the number of coins. Thus, you should have something like this:

0.05n+0.10d= 9.45

then set the number of doubled dimes to 16.65. Since you are doubling the dimes, you just multiple by 2. Since 0.10 x2 is .20, you should have:

0.05n+0.20d= 16.65

now is the algebra part. You’re going to have to set one of these equations equal to d or n. I’d suggest the first, as it is simpler

0.05n= 9.45-0.10d

divide by 0.05

n= 189 -2d

then, you plug and chug

(189-2d)0.05+0.20d= 16.65

You should get 9.45-.10d+.20d=16.65

simplify by subtracting 9.54 from 16.65, and you have

0.10d=7.

divide by .10, you get 72 dimes

now, go back and plug 72 into the first equation

.10(72)+0.05n=9.45

7.2+0.05n= 9.45

0.05n= 2.25

n=45 nickels

d= 72 dimes

double check by plugging both into both equations

0.05(45) + 0.10(72) = 9.45, this passes

0.05(45) + 0.20(72) = 16.65, this passes