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?

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Answer 1 · 2016-10-02T07:36:33

#$41#

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#