math help for my little sister?

Question

there are 62 cakes there are 3 times as many chcolate cakes than white, two fewer white than cherry, two times as many cherry as angle food, and 2 more angle food than pound cakes. how many of each cake are there?

Answer 1

Let b = brown chocolate cakes
Let w = white cakes
Let c = cherry cakes
Let a = angel food cakes
Let p = pound cakes

b = 3w
w = c - 2
c = 2a
a = p + 2

And b + w + c + a + p = 62

Let's put everything in terms of p:
a = p + 2
c = 2a = 2(p + 2) = 2p + 4
w = c - 2 = 2p + 4 - 2 = 2p + 2
b = 3w = 3(2p + 2) = 6p + 6

Now add them all together:
6p + 6 + 2p + 2 + 2p + 4 + p + 2 + p = 62

Simplify:
12p + 14 = 62
12p = 48
p = 4

Now just solve for the rest:
a = p + 2 = 6
c = 2p + 4 = 12
w = 2p + 2 = 10
b = 6p + 6 = 30

So 30 chocolate cakes, 10 white cakes, 12 cherry cakes, 6 angel food cakes and 4 pound cakes.

Answer 2

Choc + White + Cherry + Angel + Pound = 62 total cakes

Choc = 3 White ; Cherry = White +2; Cherry = 2 Angel, so Angel = (White + 2) / 2 ; Pound = Angel - 2, so Pound = (White +2) / 2 - 2 or (White - 2) / 2

Substitute into main equation:

3W + W + W + 2 + (W+2)/2 + (W - 2)/2 = 62
multiply both sides by 2:
6W + 2W + 2W + 4 + W + 2 + W - 2 = 124
collect terms:
12 W + 4 = 124 or 12W = 120 or W = 10 (white cakes)
substituting into earlier expressions find that:
Chocolate = 30, Cherry = 12, Angel = 6, and Pound = 4
Total all of them up and you get 62 total cakes.

Answer 3

3 times as many chocolate cakes than white, two fewer white than cherry, two times as many cherry as angle food, and 2 more angle food than pound cakes. Obviously you just gave us the answer in your question.

Answer 4

62 = C + W + R + A + P
C = 3W
W = R - 2
R = 2A
A = P + 2

62 = C + (C/3) + (W + 2) + (R / 2) + (A - 2)
62 = C + (C/3) + ((C/3) + 2) + ((W + 2) / 2) + ((R/2) - 2)
62 = C + (C/3) + ((C/3) + 2) + (((C/3) + 2) / 2) + (((W + 2)/2) - 2)
62 = C + (C/3) + ((C/3) + 2) + (((C/3) + 2) / 2) + ((((C/3) + 2)/2) - 2)

62 = C + C/3 + C/3 + 2 + C/6 + 1 + C/6 - 1
62 = C + 2C/3 + C/3 + 2
62 = 2C + 2
C = 30

30 = 3W
W = 10

W = R - 2
R = 12

R = 2A
A = 6

A = P + 2
P = 4

30 Chocolate, 10 White, 12 Cherry, 6 Angel Food, and 4 Pound

Answer 5

b=chocolate
w=white
c=cherry
a=angel food
p=pound

b=3w
w=c-2
c=2a
a=p+2 p=a-2

b+w+c+p+a=62
3w+w+c+p+a=62
4w+c+p+a=62
4(c-2)+c+p+a=62
4c-8+c+p+a=62
5c+p+a=70
5(2a)+p+a=70
11a+p=70
11a+a-2=70
12a=72
a=6 angel food
p=4 pound cakes
c=12 cherry
w=10 white
b=30 chocolate
6+4+12+10+30=62

Answer 6

10 white
12 cherry
6 angle
30 chocolate
4 pound

Answer 7

4 orange cakes and one apple.

Answer 8

stop it, I'm getting hungry...