Question 279858
Let {{{a}}} = ounces of 10% solution needed
Let {{{b}}} = ounces of 18% solution needed
given:
(1) {{{a + b = 32}}} ounces
(2) {{{.1a + .18b = .15*32}}}
(2) {{{.1a + .18b = 4.8}}}
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Multiply both sides of (2) by {{{100}}}
(2) {{{10a + 18b = 480}}}
Multiply both sides of (1) by {{{10}}}
and subtract from (2)
(2) {{{10a + 18b = 480}}}
(1) {{{-10a - 10b = -320}}}
{{{8b = 160}}}
{{{b = 20}}}
and, since
{{{a + b = 32}}}
{{{a + 20 = 32}}}
{{{a = 12}}}
12 ounces of 10% solution and 20 ounces of 18% solution are needed
check:
(2) {{{.1a + .18b = 4.8}}}
{{{.1*12 + .18*20 = 4.8}}}
{{{1.2 + 3.6 = 4.8}}}
{{{4.8 = 4.8}}}
OK