Question 435249
Let {{{a}}} = tons of 17% mixture needed
Let {{{b}}} = tons of 65% mixture needed
given:
(1) {{{ a + b = 10 }}} tons
(2) {{{ .17a + .65b = .362*10 }}}
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(2) {{{ .17a + .65b = 3.62 }}}
(2) {{{ 17a + 65b = 362 }}}
Multiply both sides of (1) by {{{17}}}
and subtract (1) from (2)
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(2) {{{ 17a + 65b = 362 }}}
(1) {{{ -17a - 17b = 170 }}}
{{{ 48b = 192 }}}
{{{ b = 4 }}}
and, since
(1) {{{ a + b = 10 }}}
{{{ a = 6 }}}
6 tons of 17% mixture are needed
4 tons of 65% mixture are needed
check:
(2) {{{ .17a + .65b = 3.62 }}}
(2) {{{ .17*6 + .65*4 = 3.62 }}}
{{{ 1.02 + 2.6 = 3.62 }}}
{{{ 3.62 = 3.62 }}}
OK