Question 1051796
Let {{{ a }}} = gallons of the 13% mixture needed
Let {{{ b }}} = gallons of the 18% mixture needed
--------------------------------------------
(1) {{{ ( .13a + .18b ) / 20 = .15 }}}
(2) {{{ a + b = 20 }}}
----------------------------------
(1) {{{ .13a + .18b =  .15*20 }}}
(1) {{{ .13a + .18b = 3 }}}
(1) {{{ 13a + 18b = 300 }}}
------------------------------
Multiply both sides of (2) by {{{ 13 }}}
and subtract (2) from (1)
-----------------------------------
(1) {{{ 13a + 18b = 300 }}}
(2) {{{ -13a - 13b = -260 }}}
----------------------------
{{{ 5b = 40 }}}
{{{ b = 8 }}}
and
(2) {{{ a + 8 = 20 }}}
(2) {{{ a = 12 }}}
12 gallons of the 13% mixture are needed
8 gallons of the 18% mixture are needed
---------------------------------------
check:
(1) {{{ ( .13a + .18b ) / 20 = .15 }}}
(1) {{{ ( .13*12 + .18*8 ) / 20 = .15 }}}
(1) {{{ ( 1.56 + 1.44 ) / 20 = .15 }}}
(1) {{{ 3/20 = .15 }}}
(1) {{{ 3 = .15*20 }}}
(1) {{{ 3 = 3 }}}
OK