In a basket, 3/4 of the fruits are oranges and the rest are apples. After I have away 10 oranges, there are now 1/2 as many oranges as apples. How many apples and oranges are there in the basket?

.75 fruits = orange or .75 f = oj

.25 fruits = apples or .25 f = a

oj - 10 = .5 a
so
.75 f - 10 = .125 f

.625 f = 10

f = 16 answer

now
check
12 + 4 = 16 yes
12 - 10 = 2
2 = half of 4 yes

To solve this problem, let's first assign variables to the number of oranges and apples in the basket.

Let's say the number of oranges is represented by O, and the number of apples is represented by A.

According to the given information, we know that 3/4 of the fruits in the basket are oranges. This can be written as:

O = (3/4) * (O + A)

Next, after giving away 10 oranges, there are now 1/2 as many oranges as apples. This can be written as:

(O - 10) = (1/2) * (A - 10)

We now have a system of two equations:

1) O = (3/4) * (O + A)
2) (O - 10) = (1/2) * (A - 10)

We can solve this system of equations to find the values of O and A.

Let's start by simplifying equation 1:

O = (3/4) * (O + A)
O = (3/4) * O + (3/4) * A
O = (3/4)O + (3/4)A

Next, simplify equation 2:

(O - 10) = (1/2) * (A - 10)
O - 10 = (1/2)A - 5
O = (1/2)A - 5 + 10
O = (1/2)A + 5

We now have two equations:

O = (3/4)O + (3/4)A
O = (1/2)A + 5

We can substitute the value of O from the second equation into the first equation:

(1/2)A + 5 = (3/4)(1/2)A + (3/4)A
(1/2)A + 5 = (3/8)A + (3/4)A
(1/2)A - (3/8)A - (3/4)A = -5
(4/8)A - (3/8)A - (6/8)A = -5
(-5/8)A = -5
A = (-5 * 8) / -5
A = 8

Now that we have the value of A (apples), we can substitute it back into one of the original equations to find O (oranges):

O = (1/2)A + 5
O = (1/2) * 8 + 5
O = 4 + 5
O = 9

So, there are 9 oranges and 8 apples in the basket.