Sure, let's go through each part of the question step-by-step to find the solutions:
### Part 1: Number of marbles
Given that [tex]\(\frac{3}{7}\)[/tex] of the marbles in a box are red and the remaining are green, and you know that there are 24 green marbles, we are to find the total number of marbles in the box.
1. Let [tex]\( x \)[/tex] be the total number of marbles.
2. The fraction of green marbles is [tex]\( 1 - \frac{3}{7} \)[/tex]. Since [tex]\(\frac{3}{7}\)[/tex] are red, the fraction of green marbles is [tex]\( \frac{4}{7} \)[/tex].
3. Therefore, [tex]\(\frac{4}{7} \times x = 24\)[/tex].
4. To find [tex]\( x \)[/tex], solve the equation:
[tex]\[ x = \frac{24 \times 7}{4} = 42 \][/tex]
So, there are 42 marbles in total.
### Part 2: Money left after buying the refrigerator
Given that Joe spent [tex]\(\frac{2}{5}\)[/tex] of his money on a refrigerator, and the refrigerator cost [tex]$756.00. We need to find out how much money Joe had initially and how much money he has left.
1. Let \( y \) be the total amount of money Joe had.
2. Joe spent \(\frac{2}{5}\) of his money on the refrigerator:
\[\frac{2}{5} \times y = 756.00\]
3. To find \( y \), solve the equation:
\[ y = \frac{756.00 \times 5}{2} = 1890.00 \]
4. To find the money left, subtract the cost of the refrigerator from the total money:
\[ 1890.00 - 756.00 = 1134.00 \]
So, Joe had $[/tex]1890.00 initially and has [tex]$1134.00 left after buying the refrigerator.
### Part 3: Number of mango trees
Given that there are 240 fruits in a farm, of which \(\frac{11}{20}\) are oranges and the rest are mangos, we need to determine how many mango trees there are.
1. Calculate the number of orange fruits:
\[ \frac{11}{20} \times 240 = 132 \]
2. The number of mango fruits is the total number of fruits minus the number of orange fruits:
\[ 240 - 132 = 108 \]
So, there are 108 mango trees.
In summary:
1. There are 42 marbles in total.
2. Joe had $[/tex]1890.00 initially and has $1134.00 left after buying the refrigerator.
3. There are 108 mango trees.
