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.