Question 1147027
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Let the numbers for each person be A, B, and C.  Then the given information tells us<br>
(1) A+B+C = 181<br>
(2) (4/5)A : B+28 : 4C = 2:5:8<br>
Use the ratios in (2) to get B and C in terms of A and substitute in (1).<br>
(Of course you could also get A and C in terms of B, or A and B in terms of C....)<br>
B in terms of A:<br>
{{{(4/5)A/(B+28) = 2/5}}}<br>
{{{2B+56 = 4A}}}<br>
{{{B+28 = 2A}}}<br>
{{{B = 2A-28}}}<br>
C in terms of A:<br>
{{{(4/5)A/(4C) = 2/8 = 1/4}}}<br>
{{{(4/5)A/C = 1}}}<br>
{{{C = (4/5)A}}}<br>
Substitute and solve for A:<br>
{{{A + (2A-28) + (4/5)A = 181}}}<br>
{{{(19/5)A - 28 = 181}}}<br>
{{{(19/5)A = 209}}}<br>
{{{A = (5*209)/19 = 5*11 = 55}}}<br>
Use this value of A to find B and C:<br>
{{{B = 2A-28 = 110-28 = 82}}}<br>
{{{C = (4/5)A = 44}}}<br>
Original numbers of cookies:
A = 55
B = 82
C = 44<br>