There are 32 more apples than oranges in a box. 3/5 of the oranges and 1/3 of the apples are overripe. If the number of overripe apples and the number of overripe oranges are the same, how many pieces of overripe fruit are there?
oranges --- x
apples ---- x + 32
overripe oranges = (3/5)x
overripe apples = (1/3)(x+32)
but they are the same ....
(1/3)(x+32) = (3/5)x
multiply by 15 , the LCD
5(x+32) = 9x
5x + 160 = 9x
160 = 4x
x = 40
overripe fruit = (1/3)(x+32) + (3/5)x
= (1/3)(72) + (3/5)(40) = 48
check
oranges = 40
apples = 72
overripe oranges = (3/5)(40) = 24
overripe apples = (1/3)(72) = 24
total overripe = 24+24 = 48
It’s much easier to draw 2 bars. The first is for apples and you split it into 3 equal lengths. Underneath you draw the bar for oranges which you split into 5 equal lengths, making sure that 3/5 is the same length as the 1/3 above it. Split your thirds into thirds to make ninths and now you know that 4/9 of the apples is 32 so 1/9 is 8 apples. There are 8 oranges in each 1/5 so if 3/5 are over ripe, this is 24 oranges. 1/3 of the apples are over ripe - also 24. 24+24 =48 over ripe pieces of fruit!!
Well, I guess it's a fruity situation! Let's break it down with some fruity humor.
Since there are 32 more apples than oranges, we can call the number of oranges "O" and the number of apples "A." So, we have A = O + 32.
Now, we know that 3/5 of the oranges are overripe. Let's call the number of overripe oranges "Oo." That means Oo = (3/5) * O.
Similarly, we know that 1/3 of the apples are overripe. Let's call the number of overripe apples "Ao." That means Ao = (1/3) * A.
Since the number of overripe apples and overripe oranges is the same, we can say Oo = Ao.
Now, let's substitute the values we know. Oo = (3/5) * O and Ao = (1/3) * A. So, (3/5) * O = (1/3) * (O + 32).
Let's simplify that equation. 3 * O = 5 * (O + 32).
Expanding that equation gives us 3O = 5O + 160.
Subtracting 5O from both sides gives us -2O = 160.
Dividing both sides by -2 gives us O = -80.
Oh no! Negative oranges? That doesn't sound right. Maybe it's time for some fruity improv! Let's start again and see if we get something more fruitful.
Let's break down the information given:
1. The number of apples is 32 more than the number of oranges.
2. 3/5 of the oranges are overripe.
3. 1/3 of the apples are overripe.
4. The number of overripe apples is the same as the number of overripe oranges.
Let's solve this step by step:
Step 1: Let's assume the number of oranges to be x. Therefore, the number of apples would be x + 32.
Step 2: Given that 3/5 of the oranges are overripe, we can find the number of overripe oranges:
Number of overripe oranges = (3/5) * x
Step 3: Given that 1/3 of the apples are overripe, we can find the number of overripe apples:
Number of overripe apples = (1/3) * (x + 32)
Step 4: Since the number of overripe apples and overripe oranges are the same, we can equate the two:
(3/5) * x = (1/3) * (x + 32)
Step 5: Let's solve this equation:
Multiply both sides of the equation by 15 to eliminate fractions:
9x = 5(x + 32)
Distribute:
9x = 5x + 160
Subtract 5x from both sides:
4x = 160
Divide by 4:
x = 40
Step 6: Now that we know the value of x, we can substitute it back into the equation to find the number of overripe oranges:
Number of overripe oranges = (3/5) * 40
Number of overripe oranges = 24
Step 7: Substituting the value of x into the equation, we can find the number of overripe apples:
Number of overripe apples = (1/3) * (40 + 32)
Number of overripe apples = (1/3) * 72
Number of overripe apples = 24
Step 8: Finally, we add the number of overripe oranges and overripe apples to find the total number of overripe fruits:
Total number of overripe fruits = 24 + 24
Total number of overripe fruits = 48
Therefore, there are 48 pieces of overripe fruit.
To find the number of overripe fruit, we need to first determine the number of oranges and apples in the box. Let's break down the problem step by step.
Let's assume the number of oranges in the box is represented by the variable "o". Therefore, the number of apples in the box is "o + 32" since there are 32 more apples than oranges.
Next, we need to calculate the number of overripe oranges and apples. We know that 3/5 of the oranges are overripe, so the number of overripe oranges is calculated as "3/5 * o". Similarly, 1/3 of the apples are overripe, so the number of overripe apples is "1/3 * (o + 32)".
According to the given condition, the number of overripe apples and the number of overripe oranges are the same. So, we can set up the equation:
3/5 * o = 1/3 * (o + 32)
To solve this equation, we can cross-multiply:
3 * (o + 32) = 5 * 1 * o
3o + 96 = 5o
96 = 2o
o = 48
Now that we have found the value of "o" (the number of oranges), we can substitute it back into the equation to find the number of overripe apples and oranges:
Number of overripe apples = 1/3 * (o + 32) = 1/3 * (48 + 32) = 1/3 * 80 = 80/3
Number of overripe oranges = 3/5 * o = 3/5 * 48 = 144/5
To find the total number of overripe fruits, we add the number of overripe apples and oranges:
Total number of overripe fruit = (80/3) + (144/5) = (400/15) + (432/15) = 832/15
Therefore, there are 832/15 pieces of overripe fruit.