need help badly. this is the math problem.
is the rate three-forth's cup of butter/ 3 eggs equivalent to the rate of 3 cups of butter/12 eggs?
Please show the work so I can study this equation for my next problem. thanks kindly
One way to solve this problem is with a proportion.
(3/4) / 3 = 3 / x
Cross multiply and solve for x.
(3/4)x = 9
x = 9 / (3/4)
x = 9 * (4/3)
x = 36/3 = 12
To determine if the rate three-fourths cup of butter per 3 eggs is equivalent to the rate of 3 cups of butter per 12 eggs, we need to compare the two rates.
First, let's convert the rates to fractions:
Rate 1: 3/4 cup of butter per 3 eggs
Rate 2: 3 cups of butter per 12 eggs
To compare the rates, we need to make sure they have the same units. We can do this by scaling them up or down. In this case, we're looking to convert both rates to a per egg basis.
For Rate 1:
We know that the rate is three-fourths cup of butter per 3 eggs. To find out how much butter per egg, we need to divide both the numerator and the denominator by 3.
Rate 1 (revised): (3/4) cup of butter per (3/3) egg
= (3/4) cup of butter per 1 egg
= 3/4 cup of butter per egg
Now we have the revised Rate 1 in terms of butter per egg.
For Rate 2:
The rate is three cups of butter per 12 eggs. We need to convert this to butter per egg as well. To do this, we divide both the numerator and the denominator by 12.
Rate 2 (revised): (3/12) cups of butter per (12/12) egg
= (1/4) cups of butter per 1 egg
= 1/4 cup of butter per egg
Now we have the revised Rate 2 in terms of butter per egg.
To compare the rates, we can see that both Rate 1 (3/4 cup of butter per egg) and Rate 2 (1/4 cup of butter per egg) have the same unit of butter per egg.
Therefore, the rate three-fourths cup of butter per 3 eggs is equivalent to the rate of 3 cups of butter per 12 eggs.
For your next problem, follow the same steps:
1. Convert the rates to fractions.
2. Make sure both rates have the same units.
3. Scale them up or down as needed.
4. Compare the revised rates to determine if they are equivalent.