Answer: 2500 grams
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Work Shown:
A = amount of grams of cheese you had originally
B = (2/5)*A = amount of cheese you use up after day 1
C = (3/5)*A = amount of cheese you have left over after day 1
note how B and C add back up to 'A'.
This is because 2/5+3/5 = 5/5 = 1, so,
B+C = (2/5)A+(3/5)A = (2/5+3/5)A = 1*A = A
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D = (2/5)*C = amount of cheese you use up after day 2
E = (3/5)*C = amount of cheese left over after day 2
the variables D and E add up to C
we are told that there are 900 grams of cheese left after day 2, so E = 900
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E = (3/5)*C
(3/5)*C = E
(3/5)*C = 900 ... Plug in E = 900
3C = 900*5 .... multiply both sides by 5
3C = 4500
C = 4500/3 .... divide both sides by 3
C = 1500
This means you had 1500 grams of cheese after day 1
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C = (3/5)*A
(3/5)*A = C
(3/5)*A = 1500 ... plug in C = 1500
3A = 1500*5 ... multiply both sides by 5
3A = 7500
A = 7500/3 .... divide both sides by 3
A = 2500
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You started off with 2500 grams of cheese.
After day 1, you use up (2/5)*2500 = 1000 grams of cheese and have 2500-1000 = 1500 grams left over.
After day 2, you use up (2/5)*1500 = 600 grams of cheese and have 1500-600 = 900 grams left over.
The answer is confirmed.