Question 1188238

Justin had some cards. He gave Alan 1/10 of the cards and bought another 45 
new cards. Then he used 1/3 of the new total number of cards and bought 40 new
cards. He had 160 cards in the end. How many cards did he have at first?
<pre>He's WRONG! 
Correct answer: Original number he had: <font color = red><font size = 4><b>150</font></font></b>

Let original number be C
After giving away {{{1/10}}} and buying another 45, he had {{{(9/10)C + 45}}} remaining
After using {{{1/3}}} of remainder, and buying 40 new, he had {{{(2/3)((9/10)C + 45) + 40}}} remaining
As he ended up with 160 cards, we get: {{{matrix(3,3, (2/3)((9/10)C + 45) + 40, "=", 160, 3C/5 + 30 + 40, "=", 160, 3C/5, "=", 90)}}}
                                                           3C = 5(90) ------ Cross-multiplying
                              Original number of cards, or {{{highlight_green(matrix(1,5, C, "=", 5(90)/3, "=", highlight(150)))}}}

This could've also been done with ratios instead of fractions.
If you detest fractions, then you could try that.</pre>