There are three kinds of fruit in a basket:apples, oranges, and pears. The number of apples is 1 less than the number of oranges. The number of pears is 2 times the number of apples. There are 17 fruits in the basket. How many of each kind are there?

Question

There are three kinds of fruit in a basket:apples, oranges, and pears. The number of apples is 1 less than the number of oranges. The number of pears is 2 times the number of apples. There are 17 fruits in the basket. How many of each kind are there?

Answer 1

No inequalities here.

a = o-1
p = 2a
a+o+p = 17
Let's find out how many oranges:

(o-1) + o + 2(o-1)) = 17
4o-3 = 17
4o = 20
o = 5

So, there are
4 apples
5 oranges
8 pears

Answer 2

To solve this problem, we can assign variables to the number of each fruit. Let's say:

- a represents the number of apples
- o represents the number of oranges
- p represents the number of pears

Now let's analyze the given information step by step:

1. "The number of apples is 1 less than the number of oranges."
From this information, we can write an equation: a = o - 1

2. "The number of pears is 2 times the number of apples."
Another equation can be written: p = 2a

3. "There are 17 fruits in the basket."
We know that the total number of fruits is the sum of all three types, so we have a + o + p = 17

Now we have a system of equations:
a = o - 1 (Equation 1)
p = 2a (Equation 2)
a + o + p = 17 (Equation 3)

To solve this system, we can substitute equations 1 and 2 into equation 3 to eliminate variables.

Substituting equation 1 and equation 2 into equation 3, we get:
(o - 1) + o + 2a = 17

Simplifying, we have:
2o + 2a - 1 = 17
2o + 2a = 18

Now let's examine the possible values for o and a that satisfy this equation:

o=1, a=8 (if we substitute these values into the equation, we get 18 = 18, which is true)
o=2, a=7 (gives 16 = 18, which is false)
o=3, a=6 (gives 14 = 18, which is false)
o=4, a=5 (gives 12 = 18, which is false)
o=5, a=4 (gives 10 = 18, which is false)
o=6, a=3 (gives 8 = 18, which is false)
o=7, a=2 (gives 6 = 18, which is false)
o=8, a=1 (gives 4 = 18, which is false)

So, the only solution that satisfies all the conditions is:
o = 1, a = 8

Now that we have the values of o and a, we can substitute them into equation 2 to find p:
p = 2a
p = 2 * 8
p = 16

Therefore, there are 8 apples, 1 orange, and 16 pears in the basket.