Question

(4) The weight of 4 bags of almonds and 3 bags of peanuts is 750g. The

weight of 3 bags of almonds and 5 bags of peanuts is equal to the
weight of 14 bags of peanuts. How many grams does each bag of
almonds and peanuts weigh?

Thank you in advance for any help!

Answer 1

Let x be the weight of a bag of almonds (in grams) and y be the weight of a bag of peanuts (in grams).

From the first statement, we have the equation:

4x + 3y = 750

From the second statement, we have:

3x + 5y = 14y

Simplifying the second equation, we get:

3x - 9y = 0

Now we have two equations:

4x + 3y = 750

3x - 9y = 0

We can use elimination to solve for one variable. Multiplying the second equation by 4, we get:

12x - 36y = 0

Adding this to the first equation, we get:

16x = 750

x = 46.875

Now we can substitute this value of x back into one of the equations to solve for y. Using the second equation, we get:

3(46.875) + 5y = 14y

140.625 = 9y

y = 15.625

Therefore, each bag of almonds weighs approximately 46.875 grams, and each bag of peanuts weighs approximately 15.625 grams.