Question

A box of chocolates and 2 packs of gummy bear candy weigh 460g.2 boxes of chocolates and 3 packs of gummy bear candy weigh 840g.

Answer 1

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:

1. From the first statement:
\[ c + 2g = 460 \] (Equation 1)

2. 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**