I got the answer 62 and 48 but says i am wrong

Question

 city park employee collected 1,850 cents in nickels, dimes, and quarters at the bottom of a wishing well. There were 30 nickels, and a combined total of 110 dimes and quarters. How many dimes and quarters were at the bottom of the wishing well?

dimes ??

quarters ???

can someone tell me how to solve this problem, ive been getting it wrong. I think I've missed a step maybe.

Answer 1

Let x be the number of quarters.

Since the number of quarters and dimes is 110, then 110-x is the number of dimes.

There are 30 nickels, each worth 5 cents

There are x quarters, each worth 25 cents

There are 110-x dimes, each worth 10 cents

Their total worth is 1850 cents

Translating that into a equation:

5 * 30 + 25 * x + 10 (110 - x) = 1850

150 + 25 * x + 1100 - 10*x = 1850

1250 + 15*x = 1850

15 *x = 600

x = 40

So there are 40 quarters, which means there must be 110-40 = 70 dimes.

Checking:

30 * 5 + 40 * 25 + 70 * 10 = 1850

Answer 2

Hi Caren,

you have 30 nickels , so 30 * 5 = 150 cents

total 1850 = all nickels and dime and quarters

1850 - 150 = 1700 is the sum of dimes and quarters

you now the value of dime and quarter in cent

Q = quarter = 25 cents and D= dime = 10 cents

1700 = 25 Q + 10 D and the other hand, you know the number of D and Q is 110

so you have a system with two equations

# I 110 = Q + D

# II 1700 = 25 Q + 10 D you know many methods to solve a system, i chose elimination. equation number I times -10 the add two equations

-1100 + 1700 = -10Q - 10 D + 25 Q + 10 D

600 = 15 Q both side divided by 15

40 = Q that means you have 40 quarters and 110 - 40 = 70 the number of dimes

# of quarters = 40

# of dimes = 70

I hope it is useful,

Minoo