In a box, there is a total of 82 fifty-cent coins and twenty-cent coins. The total value of the twenty-cent coins is $1.00 more than the total value of the fifty-cent coins. How many fifty-cent coins are there?

Source: Anderson Primary

In a box, there is a total of 82 fifty-cent coins and twenty-cent coins. The total value of the twenty-cent coins is $1.00 more than the total value of the fifty-cent coins. How many fifty-cent coins are there?

Source: Anderson Primary

Tan Kim Kiam

__Assume 82 20c, 0 50c __

__Base case__

82 x 20c = 1640 }

0 x 50c = 0 } difference = 1640

__Next case 81 20c, 1 50c__

81 x 20c = 1620 }

1 x 50c = 50 } difference = 1570

__Finding pattern__

1640 – 1570 = 70 (every time decreases by 70)

__Target case:__

We need to have difference of 100 or $1 as stated in the question.

We need to know 1640 – 70 how many times to get to 100

1640 – 100 = 1540 (base case of 1640 – target case of 100)

1540 ÷ 70 = 22 (22 times) Ans: 22

__ __

__More explanation and cross checking:__

22 times would mean 0 x 50c now becomes 22 x 50c

82 – 22 = 60 (22 50c means 60 20c)

60 x 20c = 1200 (total value of 20c)

22 x 50 c = 1100 (total value of 50c)

1200 – 1100 = 100 (difference is $1, confirm correct 😊)

alfretztay

1/0.20 = 5

82 – 5 = 77

2 + 5 = 7 (2 50c coins = 5 20c coins)

77/7 = 11

11 x 2 = **22**

Ans : ** 22 fifty-cent coins**.

learnwithsherpa

Total we have 82 coins (50¢ & 20¢).

2 50¢ = 5 20¢.

In order for the number of 50¢ and 20¢ to be equal, there should be sets of **7 coins **(2 50¢, 5 20¢)

82/7 = **11R5
**This implies there are 11 sets of 2 50¢ coins and 5 20¢ coins with 5 coins leftover.

For total value of 20¢ to be $1 more than 50¢, there needs to be **5 more** 20¢ than 50¢.

Total number of 20¢ coins = 11 x 5 + 5 = 60

Total number of 50¢ coins = 11 x 2 = **22**

Zappy

Can use guess-and-check method:

30x 50c coins Value = $15.00 52x 20c coins Value = $10.40

20x 50c coins Value = $10.00 62x 20c coins Value = $12.40

22x 50c coins Value = $11.00 60x 20c coins Value = $12.00

Number of 50-cent coins = __22 (ans)__