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.Find the mass of box of chocolates?

Answer 1

Let's denote the mass of a box of chocolates as \( c \) grams and the mass of a pack of gummy bear candy as \( g \) grams. We can set up the following system of equations based on the information provided.

1. From the first sentence, we have:
\[
c + 2g = 460 \quad \text{(1)}
\]

2. From the second sentence, we have:
\[
2c + 3g = 840 \quad \text{(2)}
\]

Now, we can solve this system of equations.

First, let's multiply equation (1) by 2 to align the coefficients of \( c \):
\[
2(c + 2g) = 2(460)
\]
This gives:
\[
2c + 4g = 920 \quad \text{(3)}
\]

Now, we can subtract equation (2) from equation (3):
\[
(2c + 4g) - (2c + 3g) = 920 - 840
\]
Simplifying this, we get:
\[
4g - 3g = 80
\]
\[
g = 80 \quad \text{(4)}
\]

Now that we have the value of \( g \), we can substitute it back into equation (1) to find \( c \):
\[
c + 2(80) = 460
\]
This simplifies to:
\[
c + 160 = 460
\]
Subtracting 160 from both sides gives:
\[
c = 460 - 160 = 300
\]

Thus, the mass of a box of chocolates is \( \boxed{300} \) grams.