Portioning a Blenderized Formula Batch
A home-health aide is preparing a day's supply of blenderized formula for a client who receives 3/8-cup portions through a feeding pump. The aide mixes a full batch in a 10-cup pitcher; the recipe card lists 2 1/2 level scoops of powder for every 3/4 cup of water, and the aide fills the pitcher to the 9 3/4-cup mark with water. Two and one-half cups of the finished batch have already been poured for the two morning feedings and a pump flush. The aide has 24 clean 3/8-cup portion cups on hand, and the supply company is offering 5/16-cup cups on clearance. Agency policy says a cup holding less than 1/4 cup at the end of a batch is discarded, never topped off from a new batch, and every portion must be labeled with the date and the time the batch was mixed.
1. How many full 3/8-cup portion cups can the aide fill from the formula that remains, and what happens to anything left over?
Read the worked answer
Remaining batch: 9 3/4 − 2 1/2 = 9.75 − 2.50 = 7.25, which is 7 1/4 cups.
Number of portions: 7 1/4 ÷ 3/8 = (29/4) × (8/3) = 232/12 = 19 1/3.
So 19 cups fill completely. Check the remainder: 19 × 3/8 = 57/8 = 7 1/8 cups used, leaving 7 1/4 − 7 1/8 = 1/8 cup.
Because 1/8 cup is below the 1/4-cup minimum and policy forbids topping off, that 1/8 cup (about 30 mL) is discarded, not added to any cup.
Answer: 19 labeled portion cups plus 1/8 cup discarded. Nineteen cups is well within the 24 clean cups on hand, so there is no shortage before the next delivery.
2. Using the recipe card, how many scoops of powder does the full 9 3/4-cup batch require?
Read the worked answer
Scoops scale with the water volume, not with how many portion cups the batch happens to fill.
Water units of 3/4 cup: 9 3/4 ÷ 3/4 = (39/4) × (4/3) = 13.
Scoops: 13 × 2 1/2 = 13 × 2.5 = 32.5 scoops.
Answer: 32 1/2 scoops. A scoop can be leveled at half, so this is measurable; rounding up to 33 scoops would add unneeded powder and calories, and rounding down to 32 would under-concentrate the formula. Sanity check by proportion: 2.5 scoops per 0.75 cup gives about 3.33 scoops per cup, and 9.75 × 3.33 ≈ 32.5.
3. If the aide switched to the 5/16-cup cups, how many more portions would the remaining 7 1/4 cups yield, and what clinical caution applies?
Read the worked answer
Portions with 5/16-cup cups: 7 1/4 ÷ 5/16 = (29/4) × (16/5) = 464/20 = 23.2, so 23 full cups.
Check: 23 × 5/16 = 115/16 = 7 3/16 cups; remainder 7 1/4 − 7 3/16 = 1/16 cup, discarded under the same policy.
Difference: 23 − 19 = 4 more cups.
Caution: each 5/16-cup portion holds less formula than a 3/8-cup portion (5/16 = 10/32 versus 3/8 = 12/32), so total daily volume and calories are unchanged only if the pump program and number of feedings are adjusted. The aide should not switch unilaterally; the dietitian must confirm that the smaller portion still delivers the prescribed volume and calories.