A recipe calls for 2 cups sugar to 3 cups flour. How many cups of sugar is needed for 9 cups of flour?
a.
6 cups
b. 4 cups
c. 5 cups
d 7 cups

a) 6 cups

Step-by-step explanation:

We can use a ratio for this:

sugar : flour

2 : 3

x : 9

2       3

---  =  ---

x        9

Cross multiply:

2 (9) = 3x

18 = 3x

6 = x

x = 6

To double-check, you can plug the value back into the ratio and make them fractions, then simplify to see if it gets the original amount. Here's what I'm talking about:

2 : 3

x : 9     ======>     6 : 9

move it to the other side

step-by-step explanation:

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629