Question

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 1

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 $\frac{1}{2}$ of it for the flames, and $\frac{1}{3}$ of it for the sparks.
• They needed $7\frac{3}{4}$ 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.

$18 \ pints \div 6 \ units = 3 \rightarrow \boxed{3}\boxed{3}\boxed{3}\boxed{3}\boxed{3}\boxed{3} = 18 \ pints$

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

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

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

They needed $7\frac{3}{4}$ pints of blue paint to paint the next design.

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

$\boxed{7\frac{3}{4} - 3 = ?}$

$\boxed{= \bigg( 7 + \frac{3}{4} \bigg) - 3}$

$\boxed{= 7 - 3 + \frac{3}{4}}$

$\boxed{\boxed{ \ 4\frac{3}{4}}}$

Thus, they $4\frac{3}{4}$ pints more of blue paint.

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