Question

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

Answer 1

You use simultaneous to work this out.
Say c= cinnamon red hots
g= gummbears

3c + 3g = 39
3c + 1g = 21
Since the c's are the same you subtract everything.
So 3c -3c, 3g-1g, 39-21

2g = 18 (You divide by 2 to get what g is)
g = (So 1kg of gummybears = $9)

To get cinnamon red hots, subsitute the g =9 into either the first or second equation at the top:

3c + 1g = 21
3c + 9 = 21 (we know that g=9)
3c = 12 (Subtractt 9 from 21)
c = 4 (divide both sides by 3 to get what c is)
So 1kg of cinnamon red hots = $4

Answer 2

Cinnamon Red Hits = $4 per kg

Gummy Bears = $9 per kg

Explanation:

Given parameters

Let c represent cinnamon red hots

Let g represent gummy bears

Erica Purchase:

c = 3 kg

g = 1 kg

Rate = $21

So, we can represent this on an equation as:

3c + g = 21

Irene's Purchase

c = 3 kg of

g = 3 kg

Rate = $39

So, we can represent this on an equation as:

3c + 3g = 39

Required:

What is the cost of 1 kg of each type of candy

At this point, we've derived two equations which can be solved simultaneously

3c + g = 21 --- (1)

3c + 3g = 39 ---- (2)

Subtract equation 2 from 1. This gives

3c + g = 21 --- (1)

3c + 3g = 39 ---- (2)

-----------------------------

3c - 3c + g - 3g = 21 - 39

-2g = -18

Divide through by-2

-2g/-2 = -18/-2

g = 9

Substitute 9 for g in equation 1

3c + g = 21 becomes

3c + 9 = 21

Collect like terms

3c = 21 - 9

3c = 12

Divide through by 3.

3c/3 = 12/3

c = 4

Recall that

c represent cinnamon red hots

g represent gummy bears

So,

Cinnamon Red Hits = $4 per kg

Gummy Bears = $9 per kg