Riordan started saving part of his pocket money by putting 2 coins in a money box every day. Each coin was either a 10¢ or 50¢ coin. His grandfather also put on a $1 coin in the box every 7 days. The total value of the coins after 105 days was $56.80.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his grandfather put in
= 105 ÷ 7
= 15
Total number of coins that Riordan saved
= 2 x 105 = 210 Total number of coins
= 15 + 210
= 225
(b)
Amount contributed by his grandfather
= 15 x 1
= $15
Amount that Riordan saved
= 56.80 - 15
= $41.80
$1 = 100¢
$41.80 = 4180¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 10¢ coins |
Total value of 10¢ coins |
Total value |
210
|
210 x 50 = 10500¢ |
0
|
0
|
10500¢
|
209
|
209 x 50 = 10450¢ |
1
|
1 x 10 = 10¢ |
10460¢
|
52 |
52 x 50 = 2600¢ |
158 |
158 x 10 = 1580¢ |
4180¢
|
Amount that Riordan saved if all he saved were 50¢ coins
= 210 x 50
= 10500
Big difference between the total values of 50¢ coins and 10¢ coins
= 10500 - 4180
= 6320
Small difference between the value of 50¢ coins and 10¢ coins
= 50 - 10
= 40
Number of 10¢ coins
= 6320 ÷ 40
= 158
Number of 50¢ coins
= 210 - 158
= 52
Answer(s): (a) 225; (b) 52