SOLUTION: Jessica bought some cakes from a bakery. 1/5 of them were chocolate cakes and the rest were vanilla cakes and strawberry cakes. She bought 18 strawberry cakes. There were 24 more v
Algebra ->
Percentage-and-ratio-word-problems
-> SOLUTION: Jessica bought some cakes from a bakery. 1/5 of them were chocolate cakes and the rest were vanilla cakes and strawberry cakes. She bought 18 strawberry cakes. There were 24 more v
Log On
Question 1204288: Jessica bought some cakes from a bakery. 1/5 of them were chocolate cakes and the rest were vanilla cakes and strawberry cakes. She bought 18 strawberry cakes. There were 24 more vanilla cakes than chocolate cakes.
(a) What fraction of the cakes bought were vanilla and strawberry cakes?
(b) How many vanilla cakes did Jessica buy? Found 3 solutions by greenestamps, math_tutor2020, josgarithmetic:Answer by greenestamps(13200) (Show Source):
Let c = number of chocolate cakes
Then c+24 = number of vanilla cakes
The number of strawberry cakes is given as 18
The chocolate cakes were 1/5 of the total, so the vanilla and strawberry cakes were 4/5 of the total. That means the total number of vanilla and strawberry cakes was 4 times the number of chocolate cakes:
c = number of chocolate cakes
c+24 = number of vanilla cakes
18 = number of strawberry cakes
c+(c+24)+18 = 2c+42 = total number of cakes
1/5 of that total is chocolate
(1/5)*total = number of chocolate
(1/5)*(2c+42) = c
2c+42 = 5c
42 = 5c-2c
42 = 3c
3c = 42
c = 42/3
c = 14
Jessica bought 14 chocolate cakes.
She also bought 38 vanilla cakes (because c+24 = 14+24 = 38).
In total she bought 14+38+18 = 70 cakes.
1/5 of that is (1/5)*70 = 0.2*70 = 14, to match with the chocolate cake count. It confirms our answer is correct.
(