Bobby 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 grandmother also put on a $1 coin in the box every 7 days. The total value of the coins after 49 days was $50.90.
- How many coins were there altogether?
- How many of the coins were 50¢ coins?
Total nuber of coins that his grandmother put in
= 49 ÷ 7
= 7
Total number of coins that Bobby saved
= 2 x 49 = 98 Total number of coins
= 7 + 98
= 105
(b)
Amount contributed by his grandmother
= 7 x 1
= $7
Amount that Bobby saved
= 50.90 - 7
= $43.90
$1 = 100¢
$43.90 = 4390¢
Number of 50¢ coins |
Total value of 50¢ coins |
Number of 20¢ coins |
Total value of 20¢ coins |
Total value |
98
|
98 x 50 = 4900¢ |
0
|
0
|
4900¢
|
97
|
97 x 50 = 4850¢ |
1
|
1 x 20 = 20¢ |
4870¢
|
81 |
81 x 50 = 4050¢ |
17 |
17 x 20 = 340¢ |
4390¢
|
Amount that Bobby saved if all he saved were 50¢ coins
= 98 x 50
= 4900
Big difference between the total values of 50¢ coins and 20¢ coins
= 4900 - 4390
= 510
Small difference between the value of 50¢ coins and 20¢ coins
= 50 - 20
= 30
Number of 20¢ coins
= 510 ÷ 30
= 17
Number of 50¢ coins
= 98 - 17
= 81
Answer(s): (a) 105; (b) 81