Daniel started saving part of his pocket money by putting 2 coins in a money box every day. Each coin was either a 20¢ or 50¢ coin. His father also put on a $1 coin in the box every 7 days. The total value of the coins after 98 days was $75.40.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his father put in
= 98 ÷ 7
= 14
Total number of coins that Daniel saved
= 2 x 98 = 196 Total number of coins
= 14 + 196
= 210
(b)
Amount contributed by his father
= 14 x 1
= $14
Amount that Daniel saved
= 75.40 - 14
= $61.40
$1 = 100¢
$61.40 = 6140¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 20¢ coins |
Total value of 20¢ coins |
Total value |
196
|
196 x 50 = 9800¢ |
0
|
0
|
9800¢
|
195
|
195 x 50 = 9750¢ |
1
|
1 x 20 = 20¢ |
9770¢
|
74 |
74 x 50 = 3700¢ |
122 |
122 x 20 = 2440¢ |
6140¢
|
Amount that Daniel saved if all he saved were 50¢ coins
= 196 x 50
= 9800
Big difference between the total values of 50¢ coins and 20¢ coins
= 9800 - 6140
= 3660
Small difference between the value of 50¢ coins and 20¢ coins
= 50 - 20
= 30
Number of 20¢ coins
= 3660 ÷ 30
= 122
Number of 50¢ coins
= 196 - 122
= 74
Answer(s): (a) 210; (b) 74