Answer: One kilogram of red hots is $4.
Step-by-step explanation: First of all let the red hots be represented by ‘r’ and let the gummy bears be represented by’g.’ According to the question if three kilograms of red hots and one kilogram of gummy bears cost $21, we can write this out as the following;
3r + g = 21 ———(1)
Also if three kilograms of red hots and three kilograms of gummy bears cost $39, we can write out a second equation as follows;
3r + 3g = 39 ———(2)
Now that we have a pair of simultaneous equations we shall solve for the unknowns by using the substitution method. From equation (1), make g the subject of the equation
g = 21 - 3r
Substitute for the value of g into equation (2)
3r + 3(21 - 3r) = 39
3r + 63 - 9r = 39
Collect all like terms and we have,
3r - 9r = 39 - 63
-6r = -24
Divide both sides of the equation by -6
r = 4.
Having calculated that r= 4, substitute for the value of r into equation (1)
3r + g = 21
3(4) + g = 21
12 + g = 21
Subtract 12 from both sides of the equation
g = 9.
Therefore, each kilogram of red hots cost $4, while each kilogram of gummy bears cost $9.
