A recipe calls for 3 1/2 cups of flour and 3/4 cup of sugar. If you want to make the recipe with 6 cups of flour, how much sugar will you need? Show your work.
help please and thank you.
To find out how much sugar we will need when using 6 cups of flour, we can set up a proportion.
Let's define:
x = amount of sugar needed
Based on the given recipe, we can set up a proportion using the ratio of flour to sugar:
(3 1/2 cups of flour) / (3/4 cup of sugar) = (6 cups of flour) / x
To solve the proportion, we can cross-multiply:
(3 1/2) / (3/4) = 6 / x
7/2 / 3/4 = 6 / x
Multiply the numerator of the left side by the denominator of the right side, and vice versa:
(7/2) * (4/3) = (6/x)
On the left side, simplify by multiplying the numerators and denominators:
(7 * 4) / (2 * 3) = 6 / x
28 / 6 = 6 / x
To solve for x, we can cross-multiply again:
28 * x = 6 * 6
28x = 36
Divide both sides of the equation by 28:
x = 36 / 28
Simplify the fraction (if possible):
x = 1 8/14
x = 1 4/7
Therefore, when using 6 cups of flour, you will need 1 4/7 cups of sugar.
To find out how much sugar you will need when using 6 cups of flour, we can set up a proportion using the original recipe's measurements:
(3 1/2 cups of flour) / (3/4 cup of sugar) = (6 cups of flour) / (x cups of sugar)
To solve for x (the amount of sugar needed), we can cross-multiply and solve the equation:
(3 1/2) * x = (3/4) * 6
To simplify, convert the mixed fraction into an improper fraction:
(7/2) * x = (3/4) * 6
Now, multiply both sides by the reciprocal of (7/2) to isolate x:
x = (3/4) * 6 * (2/7)
Convert the mixed fraction (6) into an improper fraction:
x = (3/4) * (6/1) * (2/7)
Multiply the numerators together and the denominators together:
x = (3 * 6 * 2) / (4 * 1 * 7)
Evaluate the numerator and denominator:
x = 36 / 28
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4:
x = 9 / 7
Therefore, when using 6 cups of flour, you will need 9/7 cups of sugar.
3.5 / 0.75 = 6/s
Cross multiply and solve for s.