Mommy preserves plums in jars so that the plums from one jar are enough for either 16 cups, or 4 pies, or half a sheet of fruit slices.

In the pantry, she has 4 such jars and wants to bake one sheet of fruit slices and 6 pies. $\mathrm{On}$ how many cups will the remaining plums be enough?

(M. Petrová)
First, we will determine how many of each type of delicacy can be prepared from all the plums:

- Four cups of plums are enough for $4 \cdot \frac{1}{2}=2$ whole trays of fruit slices.
- Four cups of plums are enough for $4 \cdot 4=16$ small cakes.
- Four cups of plums are enough for $4 \cdot 16=64$ small pastries.

In terms of plum consumption, the following equalities hold:

$$
2 \text{ trays} = 16 \text{ small cakes} = 64 \text{ small pastries.}
$$

When the mother uses the plums for one tray of fruit slices, she consumes half of all the plums. Thus, the remaining plums are enough for

$$
1 \text{ tray} = 8 \text{ small cakes} = 32 \text{ small pastries.}
$$

When she uses the plums for 6 small cakes, the remaining plums are only enough for 2 small cakes, which is a quarter of the previous amount. Therefore, from the remaining plums, she can bake

$$
2 \text{ small cakes} = 8 \text{ small pastries.}
$$

Scoring suggestion. 2 points for expressing the amount of each type of delicacy that can be baked from all the plums; 1 point each for expressing the consumption of plums for 1 tray and 6 small cakes; 2 points for expressing the consumption of plums for small pastries and the conclusion.

Note. The initial conversion ratios can also be written as follows:

$$
1 \text{ tray} = 8 \text{ small cakes, } 1 \text{ small cake} = 4 \text{ small pastries.}
$$

The previous considerations can then be simplified as follows:

After baking a tray of fruit slices, the remaining plums are enough for 1 tray, i.e., 8 small cakes. After baking 6 more small cakes, the remaining plums are enough for 2 small cakes, i.e., 8 small pastries.

For such a procedure, score 2 points for each of the three steps mentioned.

Another solution. We will calculate the consumption of plums in cups:

Since one cup of plums is enough for half a tray of fruit slices, one tray requires two cups. For further use, 2 cups remain.

Since one cup is enough for 4 small cakes, 6 small cakes require one and a half cups. For further use, half a cup remains.

Since one cup is enough for 16 small pastries, from the remaining half cup, 8 small pastries can be baked.

Scoring suggestion. 2 points for the observation that after baking a tray, 2 cups remain; 2 points for the observation that after baking 6 more small cakes, half a cup remains; 2 points for the calculation and conclusion.