David has 5-cent coins and 10-cent coins. The total value of all his coins is $37. He has 10 less 5-cent coins than 10-cent coins. How many coins does he have altogether?
|
5-cent |
10-cent |
Total |
Number |
1 u |
1 u + 10 |
2 u + 10 |
Value |
5 |
10 |
|
Total value |
5 u |
10 u + 100 |
15 u + 100 |
$1 = 100¢
$37 = 37 x 100 = 3700¢
David has 10 more 10-cent coins than 5-cent coins.
Number of 5-cent coins = 1 u
Number of 10-cent coins = 1 u + 10
Total value of 5-cent coins
= 5 x 1 u
= 5 u
Total value of 10-cent coins
= 10 x (1 u + 10)
= 10 u + 100
Total value of the coins
= 5 u + 10 u + 100
= 15 u + 100
15 u + 100 = 3700
15 u = 3700 - 100
15 u = 3600
1 u = 3600 ÷ 15 = 240
Total number of coins
= 1 u + (1 u + 10)
= 2 u + 10
= 2 x 240 + 10
= 480 + 10
= 490
Answer(s): 490