SOLUTION: There are 1580 adults and children on a ship. 60% of them are adults.when the ship stops at the harbour, some of the adults alight and the percentage of the adults remaining on the

Question 1164217: There are 1580 adults and children on a ship. 60% of them are adults.when the ship stops at the harbour, some of the adults alight and the percentage of the adults remaining on the ship decreases to 20%. How many adults alight from the ship......??
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
there are 1580 adults and children on the ship.
60% of them are adults.
that makes .6 * 1580 = 948 adults.
some of the adults get off the ship and the percentage of the adults remaining on the ship becomes 20%.
let x = the number of adults that left the ship.
your equation is 948 - x = .20 * (1580 - x)
that means that, out of the 948 adults that are on the ship, x left. when x left, 1580 - x people (adults and children) are still on the ship, and the number of adults is now 20% of that remaining number.
the equation to solve is 948 - x = .20 * (1580 - x)
simplify to get 948 - x = .20 * 1580 - .20 * x
simplify further to get 948 - x = 316 - .20 * x
add x to both sides of the equation and subtract 316 from both sides of the equation to get 948 - 316 = x - .20 * x
simplify to get 632 = .80 * x
solve for x to get x = 632 / .80 = 790
that's the number of adults that left the ship.
to confirm, do the following:
the total number of adults and children on the ship was 1580.
60% of those were adults, so the number of adults is .6 * 1580 = 948.
790 adults left the ship.
that means that 1580 - 790 = 790 adults and children still on the ship.
out of those 790, 948 - 790 = 158 are adults.
158 / 790 = .2
this means 20% of the adults and children still on the ship are adults.
you were asked how many adults left (alighted from) the ship.
the answer is 790.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
There are 1580 adults and children on a ship. 60% of them are adults.when the ship stops at the harbour, some of the adults alight and the percentage of the adults remaining on the ship decreases to 20%. How many adults alight from the ship......??

With 60% of the 1,580 individuals on board being adults, we get .6(1,580) = 948 adults
Let number of adults that alit be A
Then the number of adults that remained = 948 - A, and the remaining individuals on board = 1,580 - A
We then get:
.2(1,580 - A) = 948 - A ------- Cross-multiplying
316 - .2A = 948 - A
- .2A + A = 948 - 316
.8A = 632
Number of adults that alit, or
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