A chef uses 2 cups of broth for 13
cup of rice. The chef is making a big batch of rice and using 6 cups of rice. How many cups of broth are needed?(1 point)
Responses
36 cups
36 cups
2 cups
2 cups
12 cups
12 cups
6 cups
12 cups
To calculate the amount of broth needed for the batch of rice, we can set up a ratio using the given information.
The ratio of broth to rice is 2 cups of broth for 13 cup of rice.
We can write this ratio as:
2 cups of broth / 13 cups of rice
To find the amount of broth needed for 6 cups of rice, we can set up a proportion using the ratio:
2 cups of broth / 13 cups of rice = x cups of broth / 6 cups of rice
Cross-multiplying, we get:
2 cups of broth * 6 cups of rice = 13 cups of rice * x cups of broth
12 cups of broth = 78 cups of rice * x cups of broth
Dividing both sides by 78 cups of rice, we get:
x cups of broth = 12 cups of broth / 78 cups of rice
Simplifying this result, we find:
x cups of broth ≈ 0.154 cups of broth
So, the chef would need approximately 0.154 cups of broth for 6 cups of rice.
To find out how many cups of broth are needed for 6 cups of rice, we can set up a proportion based on the chef's original ratio of 2 cups of broth for 13 cups of rice.
The ratio can be written as:
2 cups of broth / 13 cups of rice = x cups of broth / 6 cups of rice
To solve for x, we can cross-multiply:
2 cups of broth * 6 cups of rice = 13 cups of rice * x cups of broth
This simplifies to:
12 cups of broth = 78 cups of rice * x
Next, we can isolate x:
x = (12 cups of broth) / 78 cups of rice
x ≈ 0.154 cups of broth per cup of rice
Therefore, for 6 cups of rice, the chef would need approximately:
6 cups of rice * 0.154 cups of broth = 0.924 cups of broth
Rounding to the nearest whole number, the chef would need 1 cup of broth for 6 cups of rice.