Let the amount each had at first be \(x\). Both end with the same amount left.<br><br>
[[model:questions/solutions/q10426.png]]<br><br>
Ben: After spending $80, remainder = \(x - 80\). Spent 25% of remainder on snacks, so left = 75% of \((x - 80) = 0.75(x - 80)\).<br>
Chloe: Spent 40% on a bag, so left = 60% of \(x = 0.6x\). Then spent $30 on a book, so left = \(0.6x - 30\).<br><br>
Equating:<br>
&bull; \(0.75(x - 80) = 0.6x - 30\)<br>
&bull; \(0.75x - 60 = 0.6x - 30\)<br>
&bull; \(0.15x = 30\)<br>
&bull; \(x = 30 \div 0.15 = 200\)<br><br>
Each of them had $200 at first.<br>
Check: Ben: $200 − $80 = $120; 25% of $120 = $30; left = $90. Chloe: 40% of $200 = $80; $200 − $80 = $120; $120 − $30 = $90. Both equal. ✓