Question

A jar contains 5-gram bolts and 10-gram bolts. the contents of the jar weigh 3.8 kg. if there are 460 bolts, how many 10-gram bolts are there in the jar? (convert kg to grams.)

Answer 1

The number of 10 gram bolts in the jar is 300.

Step-by-step explanation

Lets assume, the number of 5 gram bolts is
`x` and the number of 10 gram bolts is
`y`

Total weight of all bolts = 3.8 kg = (3.8 × 1000) grams = 3800 grams

So, the first equation will be:
`5x+10y= 3800 .........................( 1 )`

Now the total number of bolts is given as 460. So, the second equation will be :
`x+y=460 ............................(2)`

Solving equation (2) for y itself, we will get....

`y= 460-x`

Now, substituting this
`y= 460-x` into equation (1) in place of
`y`.....

`5x+10(460-x)= 3800\\ \\ 5x+4600-10x=3800\\ \\ -5x+4600=3800\\ \\ -5x= 3800-4600\\ \\ -5x= -800\\ \\ x= (-800)/(-5)=160`

Plugging this
`x= 160` into the equation
`y= 460-x` , we will get...

`y= 460-160=300`

So, the number of 10 gram bolts in the jar is 300.