Question 1030100
Let {{{ a }}} = cost/pound of jelly beans
Let {{{ b }}} = cost/pound of trail mix
-------------------
(1) {{{ 6a + 2b = 16 }}}
(2) {{{ 3a + 5b = 13 }}}
-------------------
Multiply both sides of (2) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 6a + 10b = 26 }}}
(1) {{{ -6a - 2b = -16 }}}
--------------------
{{{ 8b = 10 }}}
{{{ b = 1.25 }}}
and
(1) {{{ 6a + 2b = 16 }}}
(1) {{{ 3a + b = 8 }}}
(1) {{{ 3a + 1.25 = 8 }}}
(1) {{{ 3a = 6.75 }}}
(1) {{{ a = 2.25 }}}
------------------
The jelly beans cost $2.25 / pound
The trail mix costs $1.25 / pound
-------------------------------
check:
(2) {{{ 3*2.25 + 5*1.25 = 13 }}}
(2) {{{ 6.75 + 6.25 = 13 }}}
(2) {{{ 13 = 13 }}}
OK
(1) {{{ 6*2.25 + 2*1.25 = 16 }}}
(1) {{{ 13.5 + 2.5 = 16 }}}
(1) {{{ 16 = 16 }}}
OK