3 chocolate bars and 4 packets of candy weigh 200 g. 3 chocolate bars and 7 packets of candy weigh 260 g. What is the weight of a chocolate bar?
4P = 200 - 3C
3C + 7P = 260
3C + 7*(200-3C)/4 = 260
Solve for C.
x = weight of a chocolate bar
y = weight of a candy bar
Solve system of equations:
3 x + 7 y = 260
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3 x + 4 y = 200
____________
3 y = 60
y = 60 / 3 = 20 g
3 x + 4 y = 200
3 x + 4 ∙ 20 = 200
3 x + 80 = 200
3 x = 200 - 80
3 x = 120
x = 120 / 3 = 40
The weight of a chocolate bar = 40 g
To solve this problem, we can use a system of equations. Let's represent the weight of a chocolate bar as 'c' and the weight of a packet of candy as 'p'.
According to the information given:
3c + 4p = 200g (Equation 1)
3c + 7p = 260g (Equation 2)
We have two equations with two unknowns.
First, let's eliminate 'c' by subtracting Equation 1 from Equation 2:
(3c + 7p) - (3c + 4p) = 260g - 200g
3p = 60g
Now we can solve for 'p' by dividing both sides of the equation by 3:
p = 60g / 3
p = 20g
So, the weight of a packet of candy is 20 grams.
To find the weight of a chocolate bar, we can substitute the value of 'p' in either of the original equations. Let's use Equation 1:
3c + 4(20g) = 200g
3c + 80g = 200g
3c = 200g - 80g
3c = 120g
Now divide both sides of the equation by 3 to solve for 'c':
c = 120g / 3
c = 40g
Therefore, the weight of a chocolate bar is 40 grams.