A 20-kg, 5-year-old child with a hematocrit of 40% could lose how much blood and still maintain a hematocrit of 30%?

A 20-kg, 5-year-old child with a hematocrit of 40% could lose how much blood and still maintain a hematocrit of 30%?

• A. 140 mL
• B. 250 mL
• C. 350 mL
• D. 450 mL

Answer: (C)

The key idea is linking hematocrit to red cell mass and total blood volume. Hematocrit equals the red cell volume divided by total blood volume (Hct = RBCV / BV). For a 20 kg child, estimate blood volume as about 70 mL per kg, giving BV0 ≈ 1400 mL. The initial red cell volume is 0.40 × 1400 = 560 mL. If you lose some blood but then replace the lost volume with fluids to restore the blood volume back to its original 1400 mL, the final hematocrit becomes (RBCV remaining) / 1400. The RBCV remaining after losing x mL of blood (with the same 40% hematocrit) is 560 − 0.40x. Set the final hematocrit to 0.30 and solve: (560 − 0.40x) / 1400 = 0.30 560 − 0.40x = 420 0.40x = 140 x = 350 mL So, about 350 mL of blood could be lost and, with volume replacement to maintain intravascular volume, the hematocrit would drop to 30%.

The key idea is linking hematocrit to red cell mass and total blood volume. Hematocrit equals the red cell volume divided by total blood volume (Hct = RBCV / BV). For a 20 kg child, estimate blood volume as about 70 mL per kg, giving BV0 ≈ 1400 mL. The initial red cell volume is 0.40 × 1400 = 560 mL.

If you lose some blood but then replace the lost volume with fluids to restore the blood volume back to its original 1400 mL, the final hematocrit becomes (RBCV remaining) / 1400. The RBCV remaining after losing x mL of blood (with the same 40% hematocrit) is 560 − 0.40x. Set the final hematocrit to 0.30 and solve:

(560 − 0.40x) / 1400 = 0.30

560 − 0.40x = 420

0.40x = 140

x = 350 mL

So, about 350 mL of blood could be lost and, with volume replacement to maintain intravascular volume, the hematocrit would drop to 30%.