Question

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?

Answer 1

1 chair and 1 table cost `$190`

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

Explanation:

`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`