Question 1043768





The difference between two integers is 5. If the reciprocal of the smaller is added to twice the reciprocal of the larger the result is 23/66. Find the two integers.
<pre>Let the larger be L
Then smaller = L – 5
We then get: {{{1/(L - 5) + 2(1/L) = 23/66}}}_______{{{1/(L - 5) + 2/L = 23/66}}}
66L + 2(66)(L – 5) = 23L(L – 5) -------- Multiplying by LCD, 66L(L – 5)
{{{66L + 132L - 660 = 23L^2 - 115L}}}
{{{198L - 660 = 23L^2 - 115L}}}
{{{23L^2 - 115L - 198L + 660 = 0}}}
{{{23L^2 - 313L + 660 = 0}}}
{{{23L^2 - 253L - 60L + 660 = 0}}}
23L(L – 11) – 60(L – 11) = 0
(L – 11)(23L – 60) = 0
L, or {{{highlight_green(matrix(1,2, Larger, integer = 11))}}}  	   OR        L = {{{60/23}}} (ignore)
      {{{highlight_green(matrix(1,5, "Smaller", "integer:", 11 - 5, or, 6))}}}