Question

At a candy store Erica by 3 kg of cinnamon red hots in 1 kg of gummy bears for $21 meanwhile Irene by 3 kg of cinnamon red hots and 3 kg of gummy bears for $39 what is the cost of 1 kg for each type of candy

Answer 1

Answer: 1kg of cinnamon red hots is $4, while 1kg of gummy bears is $9

Step-by-step explanation: For a start, let the cinnamon red hots be represented by letter c, and let the gummy bears be represented by letter g. If Erica buys 3kg of cinnamon red hots and 1kg of gummy bears for $21 then we can express this as,

3c + g = 21

Also if Irene buys 3kg of cinnamon red hots and 3kg of gummy bears for $39, we can also express this as,

3c + 3g = 39.

We now have a pair of simultaneous equations as follows;

3c + g = 21 ———(1)

3c + 3g = 39 ———(2)

We shall use the substitution method

From equation (1), make g the subject of the equation, hence

g = 21 - 3c

Now substitute for the value of g into equation (2)

3c + 3g = 39

3c + 3(21 - 3c) = 39

3c + 63 - 9c = 39

By collecting like terms we now have

3c - 9c = 39 - 63

-6c = -24

Divide both sides of the equation by -6

c = 4

We can now substitute for the value of c into equation (1)

3c + g = 21

3(4) + g = 21

12 + g = 21

Subtract 12 from both sides of the equation

g = 9.

Therefore each kilogram of cinnamon red hots cost $4 while each kilogram of gummy bears cost $9.