Question 1090938
Hi

one tank holds 300litres more than another. If the smaller is 2/3 full it holds as much ax the larger when it is half full. What is the capacity of each.

thanks
<pre>{{{highlight_green(matrix(2,5, Smaller, tank, "holds:", 900, L, Larger, tank, "holds:", "1,200", L))}}}

<b><u>SOLUTION:</b></u>
Let capacity of smaller tank be S
Then capacity of larger tank = S + 300
At {{{2/3}}} capacity, smaller tank will have: {{{matrix(1,5, (2/3), of, S, or, 2S/3)}}}
At {{{1/2}}} capacity, larger tank will have: {{{matrix(1,5, (1/2), of, S + 300, or, (S + 300)/2)}}}
Since the above amounts are equal, we get: {{{2S/3 = (S + 300)/2}}}
2(2S) = 3(S + 300) ------- Cross-multiplying
4S = 3S + 900
S, or capacity of smaller tank = {{{highlight_green(matrix(1,2, 900, L))}}}
Capacity of larger tank = {{{highlight_green(matrix(1,6, 900, "+", "300,", or, "1,200", L))}}}