A company produces metal slabs for industrial use. the slabs come in 3 thicknesses: 5in, 10in, and 15in. the weights of each thickness for each metal are given below. metal 1: 150lbs, 300lbs, 600lbs metal 2: 130lbs, 260lbs, 390lbs metal 3: 310lbs, 620lbs, 930lbs metal 4: 140lbs, 280lbs, 420lbs for which of the metals is weight not proportional to thickness

Weights of metal 1 is not proportional to thickness.

Step-by-step explanation:

We have been given 3 thicknesses of metal slabs and the weights of each thickness for each metal. We are asked to find out which of the metals weight is not proportional to thickness.

We can see that the thicknesses of slabs are first three multiples of 5 that is 5 inches, 10 inches and 15 inches.

Now let us see which of the metals have not their weights proportional to their thicknesses.

In our first option we can see that 300 is 2 times 150 and 600 is 4 times 150 which is not proportional to thickness. In order to metal 1's weight to be proportional with it's thickness it should be 450 lbs instead of 600.

Our second metal's weight is proportional to it's thickness as 130, 260 and 390 are 3 first consecutive multiples of 130.

Our third and fourth metal's weights are also proportional to their thicknesses.

Therefore, metal 1's weight is not proportional to thickness.

Given slabs thicknesses 5in, 10in, and 15in.

Therefore, ratio of thicknesses in simplest form would be 1:2:3.

Metal 1 thicknesses = 150lbs, 300lbs, 600lbs

Dividing by 150, we get ratio of Metal 1 thicknesses = 1:2:4.

Metal 2 thicknesses = 130lbs, 260lbs, 390lbs.

Dividing by 130, we get ratio of Metal 2 thicknesses = 1:2:3.

Metal 3 thicknesses = 310lbs, 620lbs, 930lbs.

Dividing by 310, we get ratio of Metal 3 thicknesses = 1:2:3.

Metal 4 thicknesses = 140lbs, 280lbs, 420lbs.

Dividing by 140, we get ratio of Metal 4 thicknesses = 1:2:3.

We can see the ratios of thicknesses of Metal 1 are 1:2:4 but it should be 1:2:3.

Therefore, Metal 1 weight is not proportional to thickness.