Answer :
Here's how you can solve this problem step-by-step:
1. Understand the Ratio: The recipe states that you need 500 grams of potatoes for every 115 grams of flour. This is your basic ratio of ingredients.
2. Determine the Amount of Flour Needed: You want to know how much flour is needed if you have 5,000 grams of potatoes. Since the relationship between potatoes and flour is given in a ratio, you can set up a proportion:
[tex]\[
\frac{500 \text{ grams of potatoes}}{115 \text{ grams of flour}} = \frac{5000 \text{ grams of potatoes}}{x \text{ grams of flour}}
\][/tex]
3. Solve the Proportion for Flour (x):
Multiply across the known parts of the proportion to solve for [tex]\(x\)[/tex].
[tex]\[
500 \times x = 5000 \times 115
\][/tex]
[tex]\[
x = \frac{5000 \times 115}{500}
\][/tex]
Calculate this expression to find:
[tex]\[
x = 1150
\][/tex]
So, you will need 1,150 grams of flour for 5,000 grams of potatoes.
4. Calculate Total Gnocchi: The total mass of the gnocchi will be the sum of the potatoes and the flour used.
[tex]\[
\text{Total gnocchi} = 5000 \, \text{grams of potatoes} + 1150 \, \text{grams of flour} = 6150 \, \text{grams}
\][/tex]
In summary, if you use 5,000 grams of potatoes, you need 1,150 grams of flour to make a total of 6,150 grams of gnocchi.
1. Understand the Ratio: The recipe states that you need 500 grams of potatoes for every 115 grams of flour. This is your basic ratio of ingredients.
2. Determine the Amount of Flour Needed: You want to know how much flour is needed if you have 5,000 grams of potatoes. Since the relationship between potatoes and flour is given in a ratio, you can set up a proportion:
[tex]\[
\frac{500 \text{ grams of potatoes}}{115 \text{ grams of flour}} = \frac{5000 \text{ grams of potatoes}}{x \text{ grams of flour}}
\][/tex]
3. Solve the Proportion for Flour (x):
Multiply across the known parts of the proportion to solve for [tex]\(x\)[/tex].
[tex]\[
500 \times x = 5000 \times 115
\][/tex]
[tex]\[
x = \frac{5000 \times 115}{500}
\][/tex]
Calculate this expression to find:
[tex]\[
x = 1150
\][/tex]
So, you will need 1,150 grams of flour for 5,000 grams of potatoes.
4. Calculate Total Gnocchi: The total mass of the gnocchi will be the sum of the potatoes and the flour used.
[tex]\[
\text{Total gnocchi} = 5000 \, \text{grams of potatoes} + 1150 \, \text{grams of flour} = 6150 \, \text{grams}
\][/tex]
In summary, if you use 5,000 grams of potatoes, you need 1,150 grams of flour to make a total of 6,150 grams of gnocchi.