Tim 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 mother also put on a $1 coin in the box every 7 days. The total value of the coins after 84 days was $61.80.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his mother put in
= 84 ÷ 7
= 12
Total number of coins that Tim saved
= 2 x 84 = 168 Total number of coins
= 12 + 168
= 180
(b)
Amount contributed by his mother
= 12 x 1
= $12
Amount that Tim saved
= 61.80 - 12
= $49.80
$1 = 100¢
$49.80 = 4980¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 20¢ coins |
Total value of 20¢ coins |
Total value |
168
|
168 x 50 = 8400¢ |
0
|
0
|
8400¢
|
167
|
167 x 50 = 8350¢ |
1
|
1 x 20 = 20¢ |
8370¢
|
54 |
54 x 50 = 2700¢ |
114 |
114 x 20 = 2280¢ |
4980¢
|
Amount that Tim saved if all he saved were 50¢ coins
= 168 x 50
= 8400
Big difference between the total values of 50¢ coins and 20¢ coins
= 8400 - 4980
= 3420
Small difference between the value of 50¢ coins and 20¢ coins
= 50 - 20
= 30
Number of 20¢ coins
= 3420 ÷ 30
= 114
Number of 50¢ coins
= 168 - 114
= 54
Answer(s): (a) 180; (b) 54