Question 1012045

The 250 soldiers in a camp had enough food for forty days, After 10 days, 50 soldiers joined them. For how long will the remaining food last them? Solve using variation.
<pre>Let S be number of soldiers, k = constant of variation, j = amount of food, and T = time 
{{{S = k(j)/T}}}
{{{250 = k(1)/40}}}
{{{250 = k/40}}}
k = 250(40), or 10,000

Let fraction consumed after 10 days, be j
{{{S = k(j)/T}}}
{{{250 = 10000(j)/10}}}
{{{250 = 10000j/10}}}
{{{250 = 1000j}}}
j, or fraction consumed after 10 days = {{{250/1000}}}, or {{{1/4}}}

With {{{1/4}}} of food consumed {{{3/4}}} remains, and 300 (250 + 50) soldiers are in camp
{{{S = k(j)/T}}}
{{{300 = 10000(3/4)/T}}}
{{{300 = 7500/T}}}
300T = 7,500 ------- Cross-multiplying
T, or time the remaining {{{3/4}}} of food will last = {{{7500/300}}}, or {{{highlight_green(25)}}} days