Question 1019921
We have 2 gallons or 2*4 = 8 quarts of mixture
Let x be the number of quarts to replace with 100% fat to produce 5% mixture
(2%(8-x) + 100%(x) )/8 equals 5/100
That is 2% times the amount left after removing x quarts plus
100% times the same x quarts now being replaced
divided by 8, since we will continue to have 8 quarts.
This is set equal to 5/100 or 5%
{{{(0.02(8-x) + 1(x) )/8 = 5/100}}}
{{{(0.16-0.02x + x )/8 = 5/100}}}
{{{(0.16+0.98x )/8 = 5/100}}}
{{{100(0.16+0.98x ) = 8*5}}}
{{{100(0.16+0.98x ) = 40}}}
{{{16+98x  = 40}}}
add -16 to each side
{{{98x  = 24}}}
Divide each side by 98
x = 24/98
x = 0.2449 quarts
Double check
Substitute 0.2449 for x in {{{(0.02(8-x) + 1(x) )/8}}}
{{{(0.02(8-0.2449) + 1(0.2449) )/8}}}
{{{(0.02(7.7551) + 0.2449 )/8}}}
{{{(0.400002 )/8}}}
0.05000025
5.000025% , so we have it