a-plus auto body is painting desings on a customer's car. they had 18 pints of blue paint on hand. they used 1/2 of it for the flames, and 1/3 of it for the sparks. they needed 7 3/4 pints of blue paint to paint the next design. how many more pints of blue paint will they need?



Answer :

4³/₄ pints

Further explanation

Given:

A-Plus auto body is painting desigs on a customer's car.

  • They had 18 pints of blue paint on hand.
  • They used [tex]\frac{1}{2}[/tex] of it for the flames, and [tex]\frac{1}{3}[/tex] of it for the sparks.
  • They needed [tex]7\frac{3}{4}[/tex] pints of blue paint to paint the next design.

Question:

How many more pints of blue paint will they need?

The Process:

From the denominators 2 and 3 above, we get LCM = 6.

Let us draw a diagram that contains all the pints.

[tex]18 \ pints \div 6 \ units = 3 \rightarrow \boxed{3}\boxed{3}\boxed{3}\boxed{3}\boxed{3}\boxed{3} = 18 \ pints[/tex]

The flames: [tex]\frac{1}{2}[/tex] or half of 6 unit above, that is [tex]\boxed{3}\boxed{3}\boxed{3} = 9 \ pints[/tex]

The sparks: [tex]\frac{1}{3} = \frac{2}{6}[/tex] or 2 of 6 unit above, that is [tex]\boxed{3}\boxed{3} = 6 \ pints[/tex]

So, the remainder is 18 - 9 - 6 = 3 pints.

They needed [tex]7\frac{3}{4}[/tex] pints of blue paint to paint the next design.

Let us count how many more pints of blue paint will they need.

[tex]\boxed{7\frac{3}{4} - 3 = ?}[/tex]

[tex]\boxed{= \bigg( 7 + \frac{3}{4} \bigg) - 3}[/tex]

[tex]\boxed{= 7 - 3 + \frac{3}{4}}[/tex]

[tex]\boxed{\boxed{ \ 4\frac{3}{4}}}[/tex]

Thus, they [tex]4\frac{3}{4}[/tex] pints more of blue paint.

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The amount of more blue paint needed is 19 / 4 pints

They are painting a designs on a customer's car . They had 18 pints of blue paints on hand.

Amount used on flames = 1 / 2 pints

Amount used on spark = 1 / 3 pints

Therefore,

Total pints used:

  • 1 / 2 + 1 / 3 = 5 / 6

Therefore,

5 / 6 of 18 = 5  / 6 × 18 = 15 pints

Therefore, 15 pints of the paint has been used. The remaining pints of paint is 18 - 15 = 3 pints of paints.

They needed 7 3 / 4 pints of paints.

7 3 / 4 = 31 / 4 pints

Amount needed = 31 / 4  - 3 = 31 - 12/ 4 = 19 / 4 pints of paints

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