SOLVING SYSTEMS:

30 coins having a value of $3.30 consists of nickels, dimes and quarters. If there are twice as many quarters as dimes, how many coins of each kind were there?
-Thank you!

1 answer

n = nickels

q = quarters

d = dimes

There are a total of 30 coins.

n + d + q = 30

There are twice as many quarters as dimes means:

q = 2 d

n + d + q = 30

n + d + 2 d = 30

n + 3 d = 30

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

A value is $3.30

0.05 ∙ n + 0.1 ∙ d + 0. 25 ∙ q = 3.30

0.05 n + 0.1 d + 0. 25 ∙ 2 d = 3.30

0.05 n + 0.1 d + 0. 50 d = 3.30

0.05 n + 0.60 d = 3.30

Divide both sides by 0.05

n + 12 d = 66

Now you must solve system:

n + 3 d = 30

n + 12 d = 66
___________

First equation:

n + 3 d = 30

Subtract 3 d to both sides

n = 30 - 3 d

Second equation:

n + 12 d = 66

Subtract 12 d to both sides

n = 66 - 12 d

n = n

30 - 3 d = 66 - 12 d

Add 12 d to both sides

30 + 9 d = 66

Subtract 30 to both sides

9 d = 36

d = 36 / 9 = 4

n = 30 - 3 d = 30 - 3 ∙ 4 = 30 - 12 = 18

q = 2 d = 2 ∙ 4 = 8

18 nickels

4 = dimes

8 = quarters

Proof:

q = 2 d

8 = 2 ∙ 4

n + d + q = 18 + 8 + 4 = 26 + 4 = 30

0.05 ∙ n + 0.1 ∙ d + 0. 25 q =

0.05 ∙ 18 + 0.1 ∙ 4 + 0. 25 ∙ 8 =

0.9 + 0.4 + 2 = 1.3 + 2 = 3.30
Similar Questions
  1. SOLVING SYSTEMS:A bag contains nickels, dimes and quarters having a value of $3.75. If there are 40 coins in all and 3 times as
    1. answers icon 1 answer
  2. SOLVING SYSTEMS:A bag contains nickels, dimes and quarters having a value of $3.75. If there are 40 coins in all and 3 times as
    1. answers icon 1 answer
    1. answers icon 2 answers
    1. answers icon 2 answers
more similar questions