There were some black, gold and silver pencils in a box.
111 of the pencils were gold. The ratio of the number of black pencils to the number of silver pencils was 3 : 7. There were 312 fewer gold pencils than silver pencils.
- Find the ratio of the number of black pencils to the number of gold pencils to the number of silver pencils in the box.
- How many silver pencils were there?
Gold |
Black |
Silver |
Total |
1 |
10 |
11 |
|
3 |
7 |
|
1 u |
3 u |
7 u |
11 u |
(a)
Black : Gold : Silver
3 : 1 : 7
(b)
Number of fewer gold pencils than silver pencils
= 7 u - 1 u
= 6 u
6 u = 312
1 u = 312 ÷ 6 = 52
Number of silver pencils
= 7 u
= 7 x 52
= 364
Answer(s): (a) 3 : 1 : 7; (b) 364