an ice cream Parlour has 40 ice cream cups in 4 flavours Orange mango chocolate and vanilla. there are twice as many mango cups as Orange cups. the number of chocolate cups is one less than the number of orange cup. the number of vanilla cups is 7 less than the number of mango cups. how many Vanilla cups are there?
Answers
Answer:
This can be solved using the strategy used in this post:
It comes down to calculating
(5+3−13)=(73)=7⋅6⋅51⋅2⋅3=35
What we are doing is the following: We create 5 'buckets' of flavors:
−−−|−−−|−−−|−−−|−−−
Now, we want do divide the three scoops over the 5 buckets. Below, a scoop is shown as O. Some possibilities are:
O|O|||O||OOO||etc...
There are 4 borders between the buckets and 3 scoops. Thus, there are (4+33)=35 possibilitigiving 5 possibilities. (all 3 have the same flavour)
3=2+1 giving 5×4=20 possibilities. (2 with the same flavour and 1 with another)
3=1+1+1 giving (53)=10 possibilities. (all 3 have different flavour)
Answer:
Vanilla cups = 9
Step-by-step explanation:
Let we keep Orange, Mango, Chocolate and Vanilla as O, M, C and V respectively.
So,
O = x
M = 2x
C = x-1
V = 2x-7
Total no. of cups = 40
Soln:
x + 2x + (x-1) + (2x-7) = 40
3x + (x-1) + (2x-7) = 40
3x + 3x - 8 = 40
6x = 40 + 8
6x = 48
x = 48/6
x = 8
Deriving answer,
O = x = 8
M = 2x = 2*8 = 16
C = x-1 = 8-1 = 7
V = 2x-7 = 2*8 - 7 = 9
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