Question 1207222
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Aloysius had some money at first. He spent $360 on a suit. He then spent 1/7 of his remaining money on shoes and had 2/5 of his money left. How much money did he have at first?

Let original amount he had, be A
After spending $360, he had A - 360 left
After spending {{{1/7}}} of remainder, he had {{{matrix(1,10, (1 - 1/7), of, remainder, left, "=", (6/7)(A - 360), "=", 6(A - 360)/7, "=", (6A - "2,160")/7)}}}
Also, it's given that he had {{{2/5}}} of his money left. This would be: {{{matrix(1,3, (2/5)A, or, 2A/5)}}}
We now equate the 2 remainders to get: {{{matrix(1,3, (6A - "2,160")/7, "=", 2A/5)}}}
                                              7(2A) = 5(6A - 2,160) ---- Cross-multiplying
                                                14A = 30A - 5(2,160)
                                          14A - 30A = - 5(2,160)
                                              - 16A = - 5(2,160)
                             Original amount, or {{{highlight_green(matrix(1,5, A, "=", (- 5("2,160"))/(- 16), "=", highlight("$675")))}}}</pre>