solve this?

Question

Three types of fruits Candy, Chocolates, Gumdrops are available. And totally there are 20 fruits and it costs 20 cents. Candy cost 4 cents and 2 fruits of Gumdrops costs 1 cent and 4 fruits of Chocolates costs 1 cent. how many fruits of different types are there.

Answer 1

Let C, L & G be the number of fruits of Candy, Chocolates & Gumdrops respectively,

The total count is,

C+L+G = 20 ... (1)

Let x, y & z be the cost respectively.

The total cost is,

Cx + Ly + Gz = 20 ... (2)

Given,

x = 4 cents
y = 1/2 cent
z = 1/4 cent

We get,

C(4) + L(1/2) + G(1/4) = 20

Multiply by 4 throughout,

16C + 2L + G = 80 ... (3)

Take (3) - (1)

15C + L = 60

Testing possible solution,

If C=1, 15(1) + L = 60, then L has to be 45

If C=2, 15(2) + L = 60, then L has to be 30

if C=3, 15(3) + L = 50, then L has to be 15

if C=4, 15(4) + L = 60, then L has to be zero [not possible]

Testing C=1, 2 or 3 and the corresponding L in equation (1)

C + L + G = 20

if C=1, L=45, then (1)+(45)+G = 20 [not possible]

if C=2, L=30, then (2)+(30)+G = 20 [not possible]

if C=3, L=15, then (3)+(15)+G = 20, then G = 2

Therefore, the number of fruits of the different types are:

Candy: 3
Chocolates: 15
Gumdrops: 2

Answer 2

This is a set of equations

Let x = # of candy
Let y = # of gumdrops
Let z = # of Chocolates

There are two equations

x+y+z = 20 (1)

and

4x+0.5y+0.25z = 20 (2)

This is a set of 2 equations with 3 unknowns and does not produce a unique solution. However, none of x or y or z can be negative or have fractions, so we have a little more information. Assuming that you have to buy fruits of chocolate in groups of 4 then we solve by assuming a value for z.

Suppose z=0, then we have x+y=20 and 4x+0.5y =20 this means 4x+4y=80 and 3.5y = 60. y = 60/3.5 which is not an integer. Therefore z cannot equal 0.

Supose z = 4. Then x+y=16 and 4x+0.5y = 19. Therefore 4x+4y = 64 and 3.5y = 64-19 or 3.5y = 45 which is not an integer.

Suppose z = 8. Then x+y = 12 and 4x+0.5y = 18. Then reworking the equations we get 3.5y = 48-18 = 30 or y=8.57.

Suppose z = 12. Then x+y = 8 and 4x+0.5y=17 or 3.5y=32-17=15. This means y = 4.85

Suppose z = 16. Then x+y = 4 and 4x+0.5y = 16. The 3.5y = 4*4-16=0 and y=0 and x=4.

Therefore, there are 4 candies and 16 Chocolates and 0 Gumdrops in the bag.

Answer 3

3

Answer 4

3

Answer 5

4

Answer 6

20

Answer 7

fruits available

candy
chocolates
gumdrops

now

cost of fruits = 20cents
cost of candy = 4cents
cost of chocolates = 1cent
cost of gumdrops = 1cent

therefore
there are 28 types of fruits

Answer 8

20 fruits of 3+ types are there.

Answer 9

There are 3 fruits of different types, totaling 9 fruit type combinations.

Answer 10

only 3