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

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(13203)   (Show Source): You can put this solution on YOUR website!

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+24)+18 = 4(c)
c+42 = 4c
42 = 3c
c = 14

ANSWERS:
(a) 4/5
(b) c+24 = 38

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

1/5 of the cakes are chocolate
4/5 of the cakes are vanilla or strawberry

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.

Answers:
(a) 4/5
(b) 38 vanilla cakes

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!

CHOC. c/5 VAN. c-c/5-18 STRWB. 18 Total c

There were 24 more vanilla cakes than chocolate cakes.

-

-----------how many cakes she bought.

----

Chocolate:
Vanilla: ----------how many vanilla cakes

Fraction as vanilla&strawberry:
RELATED QUESTIONS
Baker Jack baked 160 cakes. 55% of them were walnut cakes and the rest were almond cakes. (answered by math_tutor2020,MathTherapy)
Hi At a bakery the ratio of cakes to muffins was 3 to 1. The bakery sold half of total... (answered by josgarithmetic,greenestamps)
Hi joan sold cookies cakes and muffins in chocolate or butter flavor. She sold 140 more... (answered by josgarithmetic)
Abu came out of the bakery shop after spending RM 320 on carrot cakes, cheese cakes and... (answered by robertb)
A factory baked some cakes. 70% of the cakes were sold at full price and 3/4 of the... (answered by ikleyn,MathTherapy)
Hi jack sold cookies, cakes and muffins in chocolate or butter flavor. He sold 140 more... (answered by stanbon,greenestamps)
You club is baking vanilla and chocolate cakes for a bake sale. They need at most 27... (answered by ReadingBoosters)
Jennifer's bakery sold half as many marble cakes as strawberry shortcakes. The price of... (answered by stanbon)
Sheena’s Bakery makes and sells cookies and cakes. It costs the store Php580 to buy the (answered by ikleyn)