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Zielflug [23.3K]
3 years ago
9

In The autumn 40% of the leaves on a tree are yellow and 24% of them are green the remaining 72 leaves are half yellow how many

leaves are on the tree
Mathematics
1 answer:
Charra [1.4K]3 years ago
3 0

Percentage of yellow leaves on a tree during Autumn = 40%

Percentage of green leaves on a tree during Autumn = 24%

Percentage of half yellow leaves on the tree during Autumn :

=  \tt100 - 40 + 24

= \tt 100 - 64

= \tt 36 \%Thus, the percentage of half yellow leaves on the tree during Autumn = 36%

Number of half yellow leaves on the tree = 36%

Let the total number of leaves on the tree be x.

Which means :

=  \tt36 \% \: of \: x = 72

=  \tt \frac{36}{100}  \times x = 72

=  \tt \frac{36 \times x}{100}  = 72

=  \tt \frac{36x}{100}  = 72

= \tt 36x = 72 \times 100

=  \tt36x = 7200

= \tt x =  \frac{7200}{36}

\color{plum} =  \tt \: x = 200

Thus, total number of leaves on the tree = 200

Number of yellow leaves on the tree :

=  \tt40 \% \: \:  of \: \:  200

=  \tt \frac{40}{100}  \times 200

= \tt   \frac{40 \times 200}{100}

= \tt  \frac{8000}{100}

\color{plum}  \tt = 80 \: yellow \:  \: leaves

Thus, total number of yellow leaves on the tree = 80

Number of green trees on the tree :

=  \tt24 \% \:  \: of \:  \: 200

= \tt  \frac{24}{100} \times 200

= \tt  \frac{24 \times 200}{100}

=  \tt \frac{4800}{100}

\color{plum} = \tt 48 \: green \:  \: leaves

Thus, the total number of green leaves on the tree = 48

Since the sum of all types of leaves form 200[80+48+72=200], we can conclude that we have found out the correct number of each type of leaf.

▪︎Therefore, <em>the total number of leaves on the tree = 200</em>

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