+58 Allan, Beth, Charis and Dollah had some paper clips each. The number of paper clips Allan had was 1/2 of the total number of paper clips Beth, Charis and Dollah had. Beth had 1/5 of the total number of paper clips Allan, Charis and Dollah had. Charis had 2/7 of the total number of paper clips Allan, Beth and Dollah had. If Dollah had 145 paper clips, find the total number of paper clips Allan and Beth had altogether.
+179 Using the given information, we can write 4 equations. Let Allan's paper clip count = a, Beth's = b, Charis' = c, and Dollah's = d
\(a=\frac{1}{2}(b+c+d)\)
\(b=\frac{1}{5}(a+c+d)\)
\(c=\frac{2}{7}(a+b+d)\)
\(d=145\)
Substituting d as 145 into each of the 3 equations, we have
\(a=\frac{1}{2}(b+c+145)\)
\(b=\frac{1}{5}(a+c+145)\)
\(c=\frac{2}{7}(a+b+145)\)
From here, it is simply substitution, elimination, to solve for each of the variables. In the end, we have
(a, b, c, d) = (174, 87, 116, 145), so Allan+Beth = 174+87 = 261
