This one is difficult. It will be better understood at Secondary 2 and up.

4 pears and 6 apples cost $6.90. This is the first case.
6 pears and 4 apples cost $7.60. This is the second case.

There are a few ways to do this. I will demonstrate two of them.

*** First Method ***

Notice that the total number of fruits is 10 in both cases.

Observe that swapping 2 apples with 2 new pears from the first case to the second case leads to an increase in the total cost of the fruits by $0.70.

This means that swapping every 1 apple with 1 new pear leads to an increase in the total cost of the fruits by $0.70/2 = $0.35.

Now, 6 pears and 4 apples cost $7.60. If we swap out 4 more apples for 4 new pears, there will now be 10 pears and no apples. In doing so, the total cost of the fruits increases by $0.35 x 4 = $1.40.

As a result, new cost of 10 pears = $7.60 + $1.40 = $9.00.

Cost of 1 pear
= $9.00/10
= $0.90

Recall that 6 pears and 4 apples cost $7.60. Now, the 6 pears cost a total of $0.90 x 6 = $5.40. The 4 apples must cost a total of $7.60 - $5.40 = $2.20.

Cost of 1 Apple
= $2.20 / 4
= $0.55

Or you can use the $0.35 increase during the swapping to calculate the cost of 1 Apple, which is $0.90 - $0.35 = $0.55.

Check that the total cost of 4 pears and 6 apples
= ($0.90 x 4) + ($0.55 x 6)
= $3.60 + $3.30
= $6.90

as required.

*** Second method ***

4 pears + 6 apples = $6.90. This is the first case.
6 pears + 4 apples = $7.60. This is the second case.

Now, we try to make the number of pears the same in both cases (note that this method also works for making the number of apples the same, which I will leave to you to try on your own).

The first common multiple of 4 pears and 6 pears is 12 pears.

Look at the first case. Since each set of 4 pears and 6 apples cost $6.90, then buying three sets (12 pears and 18 apples) cost three times as much ($6.90 x 3 = $20.70).

Look at the second case. Since each set of 6 pears and 4 apples cost $7.60, then buying two sets (12 pears and 8 apples) cost twice as much ($7.60 x 2 = $15.20).

Let’s piece the new cases together.

12 pears + 18 apples = $20.70
12 pears + 8 apples = $15.20

The difference between the two cases is the extra 10 apples with an extra cost of $20.70 - $15.20 = $5.50.

10 apples = $5.50
1 Apple = $5.50 / 10 = $0.55

So 1 apple costs $0.55.

8 apples = $0.55 x 8 = $4.40

12 pears + 8 apples = $15.20
12 pears + $4.40 = $15.20
12 pears = $15.20 - $4.40 = $10.80
1 pear = $10.80/12 = $0.90

So 1 pear costs $0.90.

You can check back the answers like I did earlier in the first method to ensure that your answers are correct.

You can also try on your own this second method by making the number of apples the same instead.