a group of people were asked to choose there favourite fruits.1/4 choose apple,1/3 banana and 2/5 orange and 3 people choose grapes. How many people were there in the group.

1/4 P + 1/3 P + 2/5 P + 3=P

solve for P

Question explain

To find out how many people were in the group, we need to determine the total number of people who chose each fruit and the number of people who chose grapes.

Given:
- 1/4 chose apple
- 1/3 chose banana
- 2/5 chose orange
- 3 people chose grapes

Let's calculate the number of people who chose each fruit:

1. For apples:
The fraction of people who chose apples is 1/4. Let's represent the total number of people as "x".
So, the number of people who chose apples = (1/4) * x = x/4.

2. For bananas:
The fraction of people who chose bananas is 1/3. Using the same logic as above, the number of people who chose bananas = (1/3) * x = x/3.

3. For oranges:
The fraction of people who chose oranges is 2/5. Using the same logic as above, the number of people who chose oranges = (2/5) * x = 2x/5.

4. For grapes:
Given that 3 people chose grapes.

Since we know the number of people who chose each fruit, we can sum them up to find the total number of people in the group:

(x/4) + (x/3) + (2x/5) + 3 = x

To solve for x, we can simplify the equation:

(15x + 20x + 24x + 60) / 60 = x

(59x + 60) / 60 = x

59x + 60 = 60x

60 = 60x - 59x

60 = x

Therefore, there were 60 people in the group.

To find out how many people were in the group, we can set up an equation.

Let's assume the total number of people in the group is "x".

Out of these, 1/4 chose apples, so the number of people who chose apples is (1/4)x.
Similarly, 1/3 chose bananas, so the number of people who chose bananas is (1/3)x.
And 2/5 chose oranges, so the number of people who chose oranges is (2/5)x.
Given that 3 people chose grapes, we can add this number to the equation as well.

So the equation can be written as:
(1/4)x + (1/3)x + (2/5)x + 3 = x

Now, we can solve this equation to find the value of x:

Multiply through by the least common denominator (LCD) of 4, 3, and 5, which is 60. This gives us:
15x + 20x + 24x + 180 = 60x

Combining like terms, we have:
59x + 180 = 60x

Subtracting 59x from both sides, we get:
180 = x

Therefore, there were 180 people in the group.