henry had 20 convertibles and 5 trucks in his miniature car collection.After Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertibles .how many trucks did his aunt buy?

So, if his convertible represent 1/5 of his collection now, that means his collection is 5 times larger than the number of convertibles. We know he has 20 convertibles... so the collection now counts 100 (5 * 20) items.

Out of 100 items, we remove the 20 convertibles to get a total of 80 trucks.

Then we subtract the initial 5 trucks... so, his aunt bought him 75 trucks.

johanrusli johanrusli · Answer 2 · 2019-09-29T05:38:48+02:00

His aunt bought 75 trucks

Further explanation

Order of Operations in Mathematics follow this following rule :

Parentheses

Exponents

Multiplication and Division

Addition and Subtraction

This rule is known as the PEMDAS method.

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

Let us tackle the problem!

Let :

Number of Additional Miniature Trucks from Henry's Aunt = X

Initial Number of Convertibles = 20

Initial Number of Trucks = 5

Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertible.

[tex]\frac{1}{5}( 20 + 5 + x ) = 20[/tex]

[tex]\frac{1}{5}( 25 + x ) = 20[/tex]

[tex]( 25 + x ) = 20 \div \frac{1}{5}[/tex]

[tex]25 + x = 20 \times \frac{5}{1}[/tex]

[tex]25 + x = \frac{20 \times 5}{1}[/tex]

[tex]25 + x = \frac{100}{1}[/tex]

[tex]25 + x = 100[/tex]

[tex]x = 100 - 25[/tex]

[tex]x = \boxed {75 ~ \texttt{trucks}}[/tex]

Conclusion:

Henry's aunt bought him 75 trucks

Learn more

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Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent