Let's denote the weight of one box of chocolates as \( c \) grams and the weight of one pack of gummy bears as \( g \) grams. We can set up the following system of equations based on the information provided:
-
From the first statement:
\[ c + 2g = 460 \] (Equation 1) -
From the second statement:
\[ 2c + 3g = 840 \] (Equation 2)
Now we can solve this system of equations.
Step 1: Solve Equation 1 for \( c \)
From Equation 1: \[ c = 460 - 2g \]
Step 2: Substitute \( c \) into Equation 2
Substituting \( c \) in Equation 2: \[ 2(460 - 2g) + 3g = 840 \]
Step 3: Distribute and simplify \[ 920 - 4g + 3g = 840 \] \[ 920 - g = 840 \]
Step 4: Solve for \( g \) \[ -g = 840 - 920 \] \[ -g = -80 \] \[ g = 80 \]
Step 5: Substitute \( g \) back to find \( c \) Substituting \( g = 80 \) into Equation 1: \[ c + 2(80) = 460 \] \[ c + 160 = 460 \] \[ c = 460 - 160 \] \[ c = 300 \]
Now, we have found the weights:
- The weight of one box of chocolates \( c = 300 \) grams
- The weight of one pack of gummy bears \( g = 80 \) grams
Summary:
- Weight of one box of chocolates: 300 grams
- Weight of one pack of gummy bears: 80 grams