The number of 10 gram bolts in the jar is 300.
Explanation
Lets assume, the number of 5 gram bolts is [tex]x[/tex] and the number of 10 gram bolts is [tex]y[/tex]
Total weight of all bolts = 3.8 kg = (3.8 × 1000) grams = 3800 grams
So, the first equation will be: [tex]5x+10y= 3800 .........................( 1 )[/tex]
Now the total number of bolts is given as 460. So, the second equation will be : [tex]x+y=460 ............................(2)[/tex]
Solving equation (2) for y itself, we will get....
[tex]y= 460-x[/tex]
Now, substituting this [tex]y= 460-x[/tex] into equation (1) in place of [tex]y[/tex].....
[tex]5x+10(460-x)= 3800\\ \\ 5x+4600-10x=3800\\ \\ -5x+4600=3800\\ \\ -5x= 3800-4600\\ \\ -5x= -800\\ \\ x= \frac{-800}{-5}=160[/tex]
Plugging this [tex]x= 160[/tex] into the equation [tex]y= 460-x[/tex] , we will get...
[tex]y= 460-160=300[/tex]
So, the number of 10 gram bolts in the jar is 300.
