How many bottles are in each group when 1700 bottles of water arranged into 4 groups with the 2nd group having 20 more than the 1st the 3rd twice the 2nd and the 4th 10 more than the 3rd?

How many bottles are in each group when 1700 bottles of water arranged into 4 groups with the 2nd group having 20 more than the 1st the 3rd twice the 2nd and the 4th 10 more than the 3rd?
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1 Answer

Answer :

let the number of bottles in the first group be BThenthe 2nd group has 1st + 20 = B + 20 bottles;the 3rd group has 2nd × 2 = 2 × (B + 20) = 2B + 40 bottles;the 4th group has 3rd + 10 = 2B + 40 + 10 = 2B + 50 bottles.The total number of bottles is the sum of the groups which is:bottles = B + B + 20 + 2B + 40 + 2B + 50 = 6B + 110But there are 1700 bottles, we can solve for B:6B + 110 = 1700→ 6B = 1590→ B = 265→ the groups contain:B = 265 bottlesB + 20 = 265 + 20 = 285 bottles2B + 40 = 530 + 40 = 570 bottles2B + 50 = 530 + 50 = 580 bottlesChecking: 265 + 285 + 570 + 580 = 1700 The groups contain 265, 285, 570 and 580 bottles respectively.
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