Question 373047
Let {{{a}}} = liters of 20% oj needed
Let {{{b}}} = liters of 5% oj needed
given:
(1) {{{a + b = 15}}}
(2) {{{(.2a + .05b)/15 = .13}}}
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From (2):
(2) {{{.2a + .05b = 1.95}}}
(2) {{{20a + 5b = 195}}}
Multiply both sides of (1) by {{{5}}}
and subtract (1) from (2)
(2) {{{20a + 5b = 195}}}
(1) {{{-5a - 5b = -75}}}
{{{15a = 120}}}
{{{a = 8}}}
And, from (1),
{{{8 + b = 15}}}
{{{b = 7}}}
8 liters of 20% oj and 7 liters of 5% oj are needed
check the answer:
(2) {{{(.2a + .05b)/15 = .13}}}
{{{(.2*8 + .05*7)/15 = .13}}}
{{{(1.6 + .35)/15 = .13}}}
{{{1.95/15 = .13}}}
{{{1.95 = 1.95}}}
OK