Question 1199194

James spent $6780 on some watches and clocks. The amount spent on watches was $2820 more than the amount spent on the clocks. He bought 3/5 as many clocks as watches. Each clock cost $25 less than each watch. What was the total number of watches and clocks bought by James?
<pre>Let amount spent on watches be W
Since a total of $6,780 was spent on watches and clocks, <font color = red><font size = 4><b>amount spent on clocks = 6,780 - W</font></font></b>
Since amount spent on watches was $2,820 more than what was spent on clocks, then <font color = red><font size = 4><b>amount spent on clocks = W - 2,820</font></font></b>
                      We then get: 6,780 - W = W - 2,820
                                     - W - W = - 2,820 - 6,780
                                        - 2W = - 9,600
Amount spent on watches =, or {{{matrix(1,5, W, "=", (- "9,600")/(- 2), "=", "$4,800")}}}
Since $4,800 was spent on watches, <font color = red><font size = 4><b>amount spent on clocks = 6,780 - 4,800 = $1,980</font></font></b>


Now, let number of watches purchased be W, and cost of each watch, C
Then number of clocks purchased = {{{matrix(1,3, (3/5)W, "=", 3W/5)}}}, and cost of each clock: C - 25

With total spent on watches being 4,800, we get: WC = 4,800 ----- eq (i)
Also, with total spent on clocks being $1,980, we get: {{{matrix(2,3, (3W/5)(C  -  25), "=", "1,980", 3WC/5 - 15W, "=", "1,980")}}}
                                                          3WC - 75W = 9,900 ----- Multiplying by LCD, 5 ----- eq (ii)
                                                     3(4,800) - 75W = 9,900 ----- Substituting 4,800 for WC in eq (ii)
                                                       14,400 - 75W = 9,900
                                                              - 75W = 9,900 - 14,400
                                                              - 75W = - 4,500
                          <font color = red><font size = 4><b>Numner of watches purchased</font></font></b>, or {{{highlight_green(matrix(1,5, W, "=", (- "4,500")/(- 75), "=", highlight(60)))}}}

                        <font color = red><font size = 4><b>Number of clocks purchased:</font></font></b>{{{highlight_green(matrix(1,7, 3W/5, "=", 3(60)/5, "=", 3(12), "=", highlight(36)))}}}</pre>