Question 1193944
Ken packed some tarts into 16 big and 18 small boxes. There is an equal number of tarts in each big box and an equal number of tarts in each small box. Each big box contained 10 more tarts than each small box. 16/25 of the tarts are packed in the big boxes. How many tarts did Ken packed in all?
<pre>Let equal number in each small box be S
Then equal number in each large box = S + 10
This makes the total in the small boxes 18S, and total in large boxes, 16(S + 10), or 16S + 160
Total number of tarts is then 18S + 16S + 160 = 34S + 160
As {{{16/25}}} of total number of tarts is in the large boxes, it follows that {{{matrix(1,3, 1 - 16/25, or, 9/25)}}} of the total
number of tarts is in the small boxes. This gives us: {{{matrix(1,3, (9/25)(34S + 160), "=", 18S)}}}
                                                          9(34S + 160) = 25(18S) ----- Cross-multiplying 
                                                         306S + 9(160) = 450S
                                                                9(160) = 450S - 306S
                                                                9(160) = 144S
                                          Number in small boxes, or {{{matrix(1,7, S,"=", 9(160)/144, "=", 160/16, "=", 10)}}}

<font size = 4><font color = blue><b>Number of tarts packed</font></font></b>: 34S + 160 = 34(10) + 160 = 340 + 160 = <font size = 4><font color = blue><b>500</font></font></b></pre>