In a basket of apples and oranges. 15% of te he fruits are rotten. 30% of the apples and 10% of the oranges were rotten. Find the ratio of the number of apples to the number of oranges.
.30a + .10o = .15(a+o)
.15a = .05o
3a = o
so as long as there are 3 times as many oranges as apples, this will work out.
check:
apples: 6 of 20
oranges: 6 of 60
total: 12 of 80 = 15%
30 of 100
30 of 300
60 of 400 = 15%
To find the ratio of the number of apples to the number of oranges, we first need to determine the fraction of the total fruits that are apples and oranges separately.
Let's assume there are a total of 100 fruits in the basket.
Given that 15% of the fruits are rotten, we know that 100 - 15 = 85 fruits are not rotten.
Now, we can find the number of rotten apples. If 30% of the apples are rotten, and the total number of apples is x, then the number of rotten apples is 0.30x.
Similarly, if 10% of the oranges are rotten, and the total number of oranges is y, then the number of rotten oranges is 0.10y.
We know that the total number of rotten fruits is 15, so we can write the equation:
0.30x + 0.10y = 15
Now, let's simplify this equation.
0.30x + 0.10y = 15
0.30x = 15 - 0.10y
0.30x = 15 - 0.10y
3x = 150 - y
3x = 150 - y
3x + y = 150
Now, we have two equations:
3x + y = 150 (Equation 1)
x + y = 100 (Equation 2)
Let's solve these two equations to find the values of x and y.
Multiply Equation 2 by -3:
-3(x + y) = -3(100)
-3x - 3y = -300
Now, add Equation 1 and the result of Equation 2:
3x + y + (-3x - 3y) = 150 - 300
-2y = -150
y = -150 / -2
y = 75
Substitute the value of y back into Equation 2:
x + 75 = 100
x = 100 - 75
x = 25
So, the number of apples (x) is 25, and the number of oranges (y) is 75.
Therefore, the ratio of the number of apples to the number of oranges is 25:75, which can be simplified to 1:3.