Mark has 21 coins in his pocket consisting of quarters, dimes, nickels, and pennies. He has at least one of each. The total amount of marks change is one dollar. How many of each coin does he have?

Mark has 1 quarter, 3 dimes, 7 nickles and 10 pennies

Step-by-step explanation:

The worth of quarter, dime, nickel, and penny is

quarter = $0.25

dime = $0.10

nickel = $0.05

penny = $0.01

Conditions to be satisfied:

1. The total number of coins should add up to 21

2. Mark has at least one of each coin

3. The total value of the coins adds up to $1

Lets say Mark has

1 quarter = 0.25

2 dimes = 2*0.10 = 0.20

4 nickles = 4*0.05 = 0.20

20 pennies = 20* 0.01 = 0.20

1. Now check if Mark has at least one of each coin

1, 2, 4, 20 (satisfied)

2. Now check if the value of coins add up to $1

0.25 + 0.20 + 0.20 + 0.20 = $0.85 (not satisfied)

3. Now check if the number of coins add up to 21

1 + 2 + 4 + 20 = 27 (not satisfied)

We have to lower the number of pennies and increase the number of dimes and nickels

1 quarter = 0.25

3 dimes = 3*0.10 = 0.30

7 nickles = 7*0.05 = 0.35

10 pennies = 10* 0.01 = 0.10

1. Now check if Mark has at least one of each coin

1, 3, 7, 10 (satisfied)

2. Now check if the value of coins add up to $1

0.25 + 0.30 + 0.35 + 0.10 = $1 (satisfied)

3. Now check if the number of coins add up to 21

1 + 3 + 7 + 10 = 21 (satisfied)

Hence all the conditions are satisfied.

Mark has 1 quarter, 3 dimes, 7 nickles and 10 pennies

Step-by-step explanation:

2.6(c - 9.5) = 5.7(2.6c + 19.3)

2.6c - 24.7 = 14.82c + 110.01

      -134.71 = 12.22c

              c = -134.71 / 12.22 ≈ - 11.0237315875613747954173...