System of Equations: Solving for the Mass of a Nut and Bolt

How can we determine the mass of a nut and bolt using a system of linear equations?

Given that 3 nuts and 6 bolts have masses of 72g, while 4 nuts and 5 bolts have a mass of 66g, what are the masses of a nut and a bolt?

Answer:

The problem can be solved by setting up a system of linear equations. Using the method of elimination, we can find that the mass of a nut (x) is 6g and the mass of a bolt (y) is 12g.

Explanation:

This problem can be solved using a system of linear equations based on the given information. The system can be set up as follows:

3x + 6y = 72, representing the mass of 3 nuts (x) and 6 bolts (y) being 72g

4x + 5y = 66, representing the mass of 4 nuts (x) and 5 bolts (y) being 66g

In order to find the values of x (mass of a nut) and y (mass of a bolt), we can use methods such as substitution, elimination, or matrix operations. By using the method of elimination, we can subtract the second equation from the first to get -x + y = 6.

Solving for y, we get y = 6 + x. Substituting this into the first equation, we get 3x + 6(6 + x) = 72. Solving this equation, we find that x = 6, which is the mass of a nut. Substituting x = 6 into y = 6 + x, we get the mass of the bolt as y = 12.