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

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.