Question

The total cost of 5 books, 6 pens and 3 calculators is $162. A pen and a calculator cost $29 and the total cost of a book and two pens is $22. Find the total cost of a book, a pen and a calculator?

Answer 1

`$41`

Explanation:

Here `5b+6p+3c = $162` ........ (i)
`1p+1c = $29` ....... (ii)
`1b+2p = $22` .......(iii)

where b = books, p = pen and c = calculators

from (ii) `1c = $29 - 1p` and from (iii) `1b = $22 - 2p`

Now put these values of c & b into eqn (i)

So, `5($22 - 2p)+6p+3($29-p) = $162`

`rarr $110-10p+6p+$87-3p = $162`

`rarr 6p-10p-3p = $162-$110-$87`

`rarr -7p = -$35`

`1p = $5`

put the value of p in eqn(ii)

`1p+1c = $29`
`$5+1c = $29`
`1c = $29-$5 = $24`

`1c=$24`

put the value of p in eqn (iii)

`1b+2p = $22`
`1b+$2*5 = $22`

`1b = $12`

Hence `1b+1p+1c = $12+$5+$24 = $41`