Ian had an equal number of butter biscuits, vanila biscuits and cream biscuits. After he ate 48 butter biscuits, some vanila biscuits and cream biscuits, there were 77 biscuits left. The number of vanila biscuits he ate was thrice the number of cream biscuits he ate. The number of vanila biscuits left was 24 more than the number of butter biscuits left. How many butter biscuits were there at first?
| |
Butter biscuits |
Vanila biscuits |
Cream biscuits |
Total biscuits |
| Before |
1 p + 48 |
1 p + 3 u + 24 |
1 p + 3 u + 24 |
|
| Change |
- 48 |
- 3 u |
- 1 u |
|
| After |
1 p |
1 p + 24 |
1 p + 24 + 1 u |
77 |
Number of vanila biscuits and butter biscuits was equal at first.
1 p + 3 u + 24 = 1 p + 48
3 u = 48 - 24
3 u = 24
1 u = 24 ÷ 3 = 8
Total number of biscuits in the end
= 1 p + 1 p + 24 + 1 p + 24 + 8
= 1 p + 1 p + 1 p + 24 + 24 + 8
= 3 p + 56
3 p + 56 = 77
3 p = 77 - 56
3 p = 21
1 p = 21 ÷ 3 = 7
Number of butter biscuits at first
= 1 p + 48
= 7 + 48
= 55
Answer(s): 55
