Question

At the supermarket, there are two kinds of flour packages. If you buy 5 packs of Package A and 6 packs of Package B, the total weight of flour is 85 kg; if you buy 10 packs of Package A and 4 packs of Package B, the total weight of flour is 90 kg. What is weight of each pack of Package A and Package B?

Answer 1

Package A: 5kg, Package B: 10kg
Use a system of equations to find the weight of each package. Set up two equations with the knowledge you know about the combined weight of the packages, using 'a' as the variable for Package A and 'b' as the variable for Package B.

5a + 6b = 85kg and 10a + 4b = 90kg

Take the second equation and solve for a, which you will use to substitute into first equation. Subtract 4b from both sides and divide everything by 10.

10a = 90kg - 4b
a = 9kg - 2/5b

Plug a = 9kg - 2/5b into the equation 5a + 6b = 85kg.

5(9kg - 2/5b) + 6b = 85kg
45kg - 2b + 6b = 85kg
45kg + 4b = 85kg
4b = 40kg
b = 10kg

Put 10kg in for b for one of the equations and solve for a.
10a + 4(10kg) = 90kg
10a + 40kg = 90kg
10a = 50kg
a = 5kg

The weight of Package A is 5kg and the weight of package B is 10kg.