Michael fills up 4 identical large and 7 identical small containers to the brim using 10.4 L of water. The amount of water he has left is 0.1 L short of filling up a large container, but it can fill up a small container with 0.3 L of water leftover.
(a) What is the difference in volume between the large container and small container ?
(b) What is the total amount of water that Michael has ?
Solution:
(a) The experiment with remaining water Michael has, when he pours the water to a large container or to a small container.
Let say volume of the remaining water = R
Michael has total = (10.4 + R) littre of water
Volume of large container = B
Volume of small container = S
R = B - 0.1 = S + 0.3
--> B - 0.1 = S + 0.3, or B - S = 0.4
Difference between large and small container = 0.4 L.
(b) From the statement
10.4 = 4 B + 7 S
= 4(S + 0.4) + 7S
= 11S + 1.6
S = 8.8 / 11 = 0.8 L
From (a), total amount = 10.4 + R = 10.4 + (0.8 + 0.3) = 11.5 L
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