Alexa has set up a lemonade stand outside her house and sells small cups and large cups of lemonade. Each small cups holds 8 ounces of lemonade and each large cup hold 16 ounces of lemonade. Alexa used 320 ounces of lemonade and sold twice as many small cups as large cups. Determine the number of small cups sold and the number of large cups sold. how do I set this equation up to get 10?​

l = large cups       amount of large cups = 16 x  ounces

small cups = 2x     amount of small cups = 8 (2x)      summed = 320 ounces

16x      +     8 (2x)       =    320        solve for 'x' the number of 16 ounce cups, the 8 ounce cups = 2x

Step-by-step explanation:

l = large cups       amount of large cups = 16 x  ounces

small cups = 2x     amount of small cups = 8 (2x)      summed = 320 ounces

16x      +     8 (2x)       =    320        solve for 'x' the number of 16 ounce cups, the 8 ounce cups = 2x

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt