Michael had an equal number of cream macarons, matcha macarons and butter macarons. After he ate 51 cream macarons, some matcha macarons and butter macarons, there were 68 macarons left. The number of matcha macarons he ate was thrice the number of butter macarons he ate. The number of matcha macarons left was 18 more than the number of cream macarons left. How many cream macarons were there at first?
| |
Cream macarons |
Matcha macarons |
Butter macarons |
Total macarons |
| Before |
1 p + 51 |
1 p + 3 u + 18 |
1 p + 3 u + 18 |
|
| Change |
- 51 |
- 3 u |
- 1 u |
|
| After |
1 p |
1 p + 18 |
1 p + 18 + 1 u |
68 |
Number of matcha macarons and cream macarons was equal at first.
1 p + 3 u + 18 = 1 p + 51
3 u = 51 - 18
3 u = 33
1 u = 33 ÷ 3 = 11
Total number of macarons in the end
= 1 p + 1 p + 18 + 1 p + 18 + 11
= 1 p + 1 p + 1 p + 18 + 18 + 11
= 3 p + 47
3 p + 47 = 68
3 p = 68 - 47
3 p = 21
1 p = 21 ÷ 3 = 7
Number of cream macarons at first
= 1 p + 51
= 7 + 51
= 58
Answer(s): 58
