Question

Explain how to solve this, step by step?

Together, a chair, a table, and a lamp cost $562. The chair costs 4 times as much as the lamp, and the table costs $23 less than the chair. Calculate the cost of the chair, the table, and the lamp.

Answer 1

The cost of chair is
`\$260`

The cost of a lamp is
`\$65`

The cost of a table is
`\$237`

Explanation:

Let

x----> the cost of chair

y----> the cost of lamp

z----> the cost of table

we know that

`x+y+z=562` ----> equation A

`x=4y` ----->
`y=x/4` -----> equation B

`z=x-23` ------> equation C

substitute equation C and equation B in equation A and solve for x

`x+(x/4)+(x-23)=562`

`(9/4)x=562+23`

`(9/4)x=585`

`x=585*4/9=\$260`

Find the value of y

`y=260/4=\$65`

Find the value of z

`z=260-23=\$237`

therefore

The cost of chair is
`\$260`

The cost of a lamp is
`\$65`

The cost of a table is
`\$237`