To determine the maximum amount of pastry mix that Gina can make, we need to understand the proportions of the ingredients in the recipe. The recipe calls for 2 parts butter and 3 parts flour, which means:
- For every 2 parts of butter, there are 3 parts of flour.
First, let's convert all measurements to the same unit. Since Gina has 1.5 kg of butter, we can convert that to grams:
\[ 1.5 \text{ kg} = 1500 \text{ g} \]
Now, Gina has:
- 1500 g of butter
- 1125 g of flour
Step 1: Determine how much pastry mix can be made based on each ingredient.
Using the ratio:
-
For 2 parts of butter (1500 g), the amount of flour needed is calculated as follows:
\[ \text{Flour needed} = \frac{3 \text{ parts of flour}}{2 \text{ parts of butter}} \times 1500 \text{ g of butter} = \frac{3}{2} \times 1500 = 2250 \text{ g of flour} \]
Since Gina only has 1125 g of flour, she does not have enough flour to use all the butter.
Step 2: Determine how much pastry mix can be made based on the available flour.
We can find out how much butter is needed for the available 1125 g of flour:
\[ \text{Butter needed} = \frac{2 \text{ parts of butter}}{3 \text{ parts of flour}} \times 1125 \text{ g of flour} = \frac{2}{3} \times 1125 = 750 \text{ g of butter} \]
Step 3: Calculate the total amount of pastry mix.
Now with 1125 g of flour and 750 g of butter, let's check the total amount of pastry mix:
\[ \text{Total pastry mix} = \text{Butter} + \text{Flour} = 750 \text{ g} + 1125 \text{ g} = 1875 \text{ g} \]
Therefore, the most pastry mix Gina can make with the available ingredients is 1875 grams.
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