Question

An electronic notice board, measuring 3m x 2m, is mounted on a square wall with sides 6m x 6m. Pablo must paint all of the wall not covered by the notice board.

A litre of paint covers 2.80m^2 of wall. Paint can be bought in 1 litre cans costing $10 each or 2.5 litre cans costing $20 each.

What is the least that Pablo can spend on paint that allows him to complete his painting job?

Answer 1

$90

Explanation:

The board is 6m^2
The wall is 36m^2

36 - 6 = 30m^2

30/2.8 = 10.714

if he buys 4 cans of 2.5 liters he will have 10 but he needs a bit more so he should buy a 1 liter can. In total this is 4*20 + 1*10 which is $90.

Answer 2

The least that Pablo can spend on paint is $90.

Explanation:

First, calculate the Area of the Wall Not Covered by the Notice Board:

The area of the wall not covered by the notice board is the same as the area of the square wall minus the area of the notice board.

`\sf \textsf{ Area of the square wall }= 6m * 6m = 36m^2`

`\sf \textsf{ Area of the notice board }= 3m * 2m = 6m^2`

Now,

`\sf \textsf{ Area of wall not covered }= 36m^2 - 6m^2 = 30m^2`

Secondly, Determine the Number of Litres Needed:

Now, we need to determine how many litres of paint are needed to cover 30m^2.

Given that 1 litre of paint covers 2.80m^2, we can calculate the number of litres required:

`\sf \begin{aligned} \textsf{ Number of litres} &\sf = \frac{\textsf{ (Area to be painted) }}{\textsf{(Coverage per litre) }}\\\\&\sf = (30m^2 )/( 2.80m^2/litre )\\\\&\sf = 10.71 \textsf{ litres in 2 d.p} \end{aligned}`

Since Pablo cannot buy a fraction of a litre, he will need at least 11 litres of paint.

Finally, calculate the Cost:

Pablo can buy either 1-litre cans for $10 each or 2.5-litre cans for $20 each.

Let's check both:

• 
  `\textsf{ If he buys 11 one-liter cans, the cost will be:}\\\sf 11 * \$10 = \$110.`

It's expensive in the case of a 2-litre can, so

Let's find the number of cans of 2.5-litre cans costing $20 each if he buys two-and-a-half-litre cans.

`\sf \textsf{ No. of 2.5-litre cans} = \frac{\textsf{Total litres of paints }}{2.5}`

`\sf \textsf{ No. of 2.5-litre cans} = ( 10.71)/(2.5)`

`\sf \textsf{ No. of 2.5-litre cans} =\sf 4.284`

Since Pablo cannot buy a fraction of cans, he will need at least 4 2.5-litre cans and he can buy the remaining paints of 1-litre cans.

The least amount Pablo can spend on paint :

=cost of 4 2.5 litre cans + cost of 1 1-litre can

`\sf = 4 * \$20 + 1 * \$10`

`\sf = \$80+ \$10`

Therefore, the least that Pablo can spend on paint to complete his painting job is $90 if he combines both.