Luke 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 mother also put on a $1 coin in the box every 7 days. The total value of the coins after 105 days was $66.80.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his mother put in
= 105 ÷ 7
= 15
Total number of coins that Luke saved
= 2 x 105 = 210 Total number of coins
= 15 + 210
= 225
(b)
Amount contributed by his mother
= 15 x 1
= $15
Amount that Luke saved
= 66.80 - 15
= $51.80
$1 = 100¢
$51.80 = 5180¢
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¢
|
77 |
77 x 50 = 3850¢ |
133 |
133 x 10 = 1330¢ |
5180¢
|
Amount that Luke 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 - 5180
= 5320
Small difference between the value of 50¢ coins and 10¢ coins
= 50 - 10
= 40
Number of 10¢ coins
= 5320 ÷ 40
= 133
Number of 50¢ coins
= 210 - 133
= 77
Answer(s): (a) 225; (b) 77