Question

test yourself! practice tool
at a candy store, erika bought 3 kilograms of cinnamon red hots and 1 kilogram of gummy bears for $21.00. meanwhile, irene bought 3 kilograms of cinnamon red hots and 3 kilograms of gummy bears for $39.00. what is the cost of one kilogram of each type of candy?
red hots:
gummy bears:

Explanation:

Step1: Define Variables

Let \( r \) be the cost of 1 kg of red hots (in dollars) and \( g \) be the cost of 1 kg of gummy bears (in dollars).

Step2: Set Up Equations

From Erika's purchase: \( 3r + g = 21 \) (Equation 1)
From Irene's purchase: \( 3r + 3g = 39 \) (Equation 2)

Step3: Solve for \( g \)

Subtract Equation 1 from Equation 2:
\( (3r + 3g) - (3r + g) = 39 - 21 \)
\( 2g = 18 \)
\( g = \frac{18}{2} = 9 \)

Step4: Solve for \( r \)

Substitute \( g = 9 \) into Equation 1:
\( 3r + 9 = 21 \)
\( 3r = 21 - 9 = 12 \)
\( r = \frac{12}{3} = 4 \)

Answer:

Red hots: \(\$4\) per kilogram
Gummy bears: \(\$9\) per kilogram