The cost of 6 identical chairs, 5 identical lamps and 1 table is $505. The cost of 2 such chairs and 1 table is $228, while 1 chair and 1 lamp cost $63. What is the total cost of 1 chair and 1 table? What is the total cost of 1 table, 1 lamp and 1 chair?

Question

1563 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-28T08:19:32

1 chair and 1 table cost $$190$

1 chair, 1 table and 1 lamp cost $$215$

$rarr$ 6 chairs + 5 lamps + 1 table cost $505.

But we also know that

$rarr$ 2 chairs and 1 table cost $228.
Let's remove these items and some money from the first group.

6 chairs -2 chairs = 4 chairs
$$505 - $228 = $277$

There will be now be only
$rarr$ 4 chairs and 5 lamps for $277.

$rarr$ 1 chair and 1 lamp together cost $63.

So, 4 chairs and 4 lamps will be $4 xx $63= $252$
But 4 chairs and 5 lamps cost $277$

Which means that 1 lamp is the difference between $277 and 252$

1 lamp costs $$25$
$rarr$ 1 chair and 1 lamp together cost $63
$rarr$ 1 chair and $$25$ is $$63$

So, 1 chair costs $$38$

$rarr$ 2 chairs and 1 table cost $$228$
Take away the price of the 2 chairs @ $$38$

$228- 2 xx 38 = $152$

NOW we have:
a lamp costs ... $25.
a chair costs ...$38
a table costs ...$152

1 chair and 1 table = $$190$

1 chair, 1 table and 1 lamp costs $$215$