Question 1203331
<pre>
Betty baked some cheese buns and butter buns. After she sold 1/3 of the cheese buns and 2/5 of the butter buns, she had 50% as many butter buns as cheese buns left. What fraction of the buns baked was butter buns?

Let number of cheese, and butter buns baked, be C and B, respectively
As she sold {{{1/3}}} of cheese buns, {{{matrix(1,5, 2/3, of, C, or, 2C/3)}}} remained
As she sold {{{2/5}}} of butter buns, {{{matrix(1,5, 3/5, of, B, or, 3B/5)}}} remained
Since 50% as many butter as cheese remained, we get: {{{matrix(2,3, 3B/5, "=", .5(2C/3), 3B/5, "=", C/3)}}}
                                                      5C = 9B ---- Cross-multiplying
                      Number of cheese buns baked, or {{{matrix(1,5, C, "=", 9B/5, or, 1.8B)}}}

Number of buns baked: C + B = 1.8B + B = 2.8B

Number of butter buns baked: B
Fraction of buns baked that were butter: {{{highlight_green(matrix(1,7, B/(2.8B), "=", 1/2.8, "=", 10/28, "=", highlight(5/14)))}}}</pre>