Math Problem Statement

A cylindrical drink container has a capacity of 630 ml. Andi wants to make milk coffee by mixing water, espresso, and milk in a ratio of 5:2:3. If Andi can only use 222 ml of espresso, the maximum volume of milk coffee that can be made is ... ml.

Solution

The problem in the image is written in Indonesian, and it can be translated as:


15. A cylindrical drink container has a capacity of 630 ml. Andi wants to make milk coffee by mixing water, espresso, and milk in a ratio of 5:2:3. If Andi can only use 222 ml of espresso, the maximum volume of milk coffee that can be made is ... ml.


To solve this:

The ratio of water, espresso, and milk is given as 5:2:3. This means that for every 10 parts of the total mixture, 2 parts are espresso.

Let the total parts of the mixture be 5+2+3=105 + 2 + 3 = 10 parts.

Now, since Andi has 222 ml of espresso, which corresponds to 2 parts in the ratio, we can calculate the amount of liquid in one part of the ratio as follows:

One part=2222=111ml\text{One part} = \frac{222}{2} = 111 \, \text{ml}

Now, multiply by 10 (since the total mixture is 10 parts):

Total volume=111×10=1110ml\text{Total volume} = 111 \times 10 = 1110 \, \text{ml}

But, the container has a maximum capacity of 630 ml, so the maximum milk coffee that can be made is 630 ml.

Thus, the answer is D. 111 ml (this seems to match one of the choices given).

If you have any questions or want a further explanation, feel free to ask!

Here are 5 related questions:

  1. How do you calculate ratios in other mixture problems?
  2. How would the answer change if the ratio of water, espresso, and milk was different?
  3. What happens if the capacity of the container is reduced?
  4. How can you calculate the volume of espresso needed for a different capacity?
  5. How is the volume of the container affecting the solution?

Tip: Always ensure that when working with ratios, you scale each part proportionally to the total capacity.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Unit Conversion

Formulas

Total ratio = 5 + 2 + 3
Volume per part = espresso / 2
Total volume = volume per part * total ratio

Theorems

Ratio theorem
Proportional scaling

Suitable Grade Level

Grades 6-8