There are some apples and oranges in a fruit basket. If Eve eats 2 apples, the number of apples left is 1/5 of the total number of fruits left in the fruit basket. If Eve eats 1 orange, the number of apples left is 2/7 of the total number of fruits left in the fruit basket. How many apples and oranges are there in the fruit basket?
a-2 = 1/5 (a-2 + o)
a = 2/7 (a + o-1)
a = 6
o = 16
16 + 6 = 22 fruits altogether
To solve this problem, let's assign variables to represent the number of apples and oranges in the fruit basket.
Let's say the number of apples is A, and the number of oranges is O.
According to the given information, when Eve eats 2 apples, the number of apples left is 1/5 of the total number of fruits left in the fruit basket. This can be expressed as:
(A - 2) = (1/5) * (A + O) ------ Equation 1
Similarly, when Eve eats 1 orange, the number of apples left is 2/7 of the total number of fruits left in the fruit basket. This can be expressed as:
A = (2/7) * (A + O) ------ Equation 2
Now, we have two equations with two variables. Let's solve them to find the values of A and O.
Simplifying Equation 1:
Multiply both sides by 5:
5(A - 2) = A + O
5A - 10 = A + O
Simplifying Equation 2:
Multiply both sides by 7:
7A = 2(A + O)
7A = 2A + 2O
Now, we can solve these equations simultaneously.
Rearrange the terms in Equation 1:
4A - O = 10 ------ Equation 3
Substitute Equation 3 into Equation 2:
7A = 2A + 2(4A - 10)
7A = 2A + 8A - 20
7A - 2A - 8A = -20
-3A = -20
A = (-20)/(-3) = 20/3 = 6.67 (approximately)
Since the number of apples cannot be in decimal form, let's assume the number of apples is 6.
Substitute the value of A into Equation 3 to find O:
4(6) - O = 10
24 - O = 10
-O = 10 - 24
-O = -14
O = 14
Therefore, the number of apples in the fruit basket is 6, and the number of oranges is 14.
Compare the two ratios—expand/reduce so that the unchanged quantity is represented by the same number in ratio. Note the change in ratio units.
The common quantity in those ratios is the unchanged number of oranges. The ratio units of the oranges are already equal, so the ratios may be combined as is—no need to reduce/expand the ratios in order to compare them.