Question 198835
Let {{{a}}}= ounces of brand A they need
Let {{{b}}}= ounces of brand B they need
given:
{{{.35a}}}= ounces of peanuts in brand A
{{{.25b}}}= ounces of peanuts in brand B
{{{a + b = 21}}}
{{{.29*21 = 6.09}}}= ounces of peanuts in final mixture
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In words:
(total ounces of peanuts) / (total ounces of mixture) = % peanuts
(1) {{{a + b = 21}}}
(2) {{{(.35a + .25b) / 21 = .29}}}
Multiply both sides of (2) by {{{21}}}
(2) {{{.35a + .25b = 6.09}}}
Multiply both sides of (1) by {{{.25}}}
and subtract (1) from (2)
(2) {{{.35a + .25b = 6.09}}}
(1) {{{-.25a - .25b = 5.25}}}
{{{.1a = .84}}}
{{{a = 8.4}}}
and, since
{{{a + b = 21}}}
{{{b = 21 - 8.4}}}
{{{b = 12.6}}}
They need 8.4 ounces of brand A and 12.6 ounces of brand B
check answer:
(2) {{{(.35a + .25b) / 21 = .29}}}
(2) {{{(.35*8.4 + .25*12.6) / 21 = .29}}}
{{{(2.94 + 3.15) / 21 = .29}}}
{{{6.09/21 = .29}}}
{{{.29 = .29}}}
OK