Question 1202333
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David spent $75 of his money on some t-shirts. He spent 1/4 of the remaining money on some batteries. Given that he was left with 1/3 of his original sum of money left, how much money did David have at first?

Let initial amount David had, be D
After spending $75, he had D - 75 remaining
After spending ¼remainder, he then had: ¾remainder, or ¾(D  -  75), or {{{(3D  -  225)/4}}} remaining
Since after his spending "spree," his remainder was {{{1/3}}} of his initial amount, we then get: {{{matrix(2,3, (3D  -  225)/4, "=", (1/3)D, (3D  -  225)/4, "=", D/3)}}} 
                                                                                         3(3D - 225) = 4D ----- Cross-multiplying
                                                                                            9D - 675 = 4D
                                                                                               - 675 = 4D - 9D
                                                                                               - 675 = - 5D
                                                                    Original amount David had, or {{{highlight_green(matrix(1,5, D, "=", (- 675)/(- 5), "=", highlight("$135")))}}}</pre>