i need help with my son's test question !!

Question

in a fruit stall,3/5 of the fruits were oranges and 3/8 of the remaining fruits were lemons, the rest were apples.there were 133 more oranges than apples.how much fruits were in the stall altogether?

Answer 1

Step 1. Let's figure out what proportion of the total fruit are lemons.

We know that 3/5 of the total fruit are oranges and that 3/8 of the remaining fruit are lemons. So how much of the fruit is remaining after we take out the oranges? 1 - 3/5 = 2/5. So the remaining fruit after we remove the oranges is 2/5 of the total fruit. Now we know that 3/8 of this remainder (2/5) make up the lemons. That means that the proportion of lemons in the total fruit is 3/8 x 2/5 which is 6/40. We now know that 6/40 of the total fruit are lemons.

Step 2. Now let's figure out what proportion of the total fruit are apples.

Since we are dealing with proportions, we know that the sum of all the parts of a whole must equal 1. We can use this knowledge to help us determine the proportion of apples. We know 3/5 of the fruit are oranges and 6/40 are lemons. This means:

3/5 + 6/40 + proportion of apples = 1

Let's convert the fractions to the same denominator so it's easier to add. 3/5 is the same as 24/40, so:

24/40 + 6/40 + proportion of apples = 1 Now let's sum the first 2 fractions:

30/40 + proportion of apples = 1

proportion of apples = 1 - 30/40

proportion of apples = 10/40 or 1/4

Great, now we know the proportions of all the fruit. 3/5 oranges, 6/40 lemons, and 1/4 apples.

Step 3. Now we can use these numbers to determine the total amount of fruit.

We know that there are 133 more apples than oranges which we can write as:

133 + apples = oranges

From step 2, we know that apples = 1/4 of the total number of fruit which we can write as:

apples = 1/4*T

and oranges = 3/5 of the total number of fruit we we can write as:

oranges = 3/5*T

Let's substitutes these values into the equation of 133 + apples = oranges

133 + 1/4*T = 3/5*T

Let's give the fractions the same denominator for ease of calculation.

133 + 5/20*T = 12/20*T

Now we can solve for the total number of fruit!

133 = 7/20*T

T = 380

The total number of fruit is 380!

Let's double check our work to make sure this is correct. We know that oranges are 3/5 of the total fruit so 3/5 of 380 = 228. We also know that apples are 1/4 of the total fruit so 1/4 of 380= 95. We also know that 133 + apples = oranges. Does 133 + 95 = 228? Yes! We have the correct answer!

Answer 2

Let's call x the number of oranges, y the number of lemons and z the number of apples.

1- The total number of fruits is x + y + z. So, when they say "3/5 of the fruits were oranges", in equation terms, it means: x = (3/5)(x + y + z).

2- "3/8 of the remaining fruits were lemons": First, we need to understand what they mean by "remaining fruits". If the oranges count for 3/5 of all the fruits, then the remaining should count for 2/5. And out of those 2/5 of all the fruits, only 3/8 are lemons. I know it sounds complicated, but put into math terms, it's something like this: y = (3/8)(2/5)(x + y + z)

3- The rest were apples: that would mean: z = (total fruits) - x - y, which is also: z = (x + y + z) - (3/5)(x + y + z) - (3/8)(2/5)(x + y + z). However, with simplification, you'll realize that this doesn't give you more information. It will give you an equation that is equivalent to the two we've had so far.

4- We need three equations to find three unknowns, and so far we have two (and one that is not useful). The last piece of information they gave us will get us that third equation: "there were 133 more oranges than apples": x = z + 133.

That gives you a system of three equations and three unknown, that hopefully, you can solve!