Question 719846
Let {{{ a }}} = the price in dollars of a slice of pizza
Let {{{ b }}} = the price in dollars of a cola
given:
Tanisha's bill:
(1) {{{ 3a + 2b = 6 }}}
Rachel's bill:
(2) {{{ 2a + 3b = 5.25 }}}
---------------------
Multiply both sides of (1) by {{{ 3 }}}
Multiply both sides of (2) by {{{ 2 }}}
Subtract (2) from (1)
(1) {{{ 9a + 6b = 18 }}}
(2) {{{ -4a - 6b = 10.5 }}}
{{{ 5a = 7.5 }}}
{{{ a = 1.5 }}}
Plug this result back into (1) or (2)
(1) {{{ 3*1.5 + 2b = 6 }}}
(1) {{{ 4.5 + 2b = 6 }}}
(1) {{{ 2b = 1.5 }}}
(1) {{{ b = .75 }}}
$1.50 = the price of a slice of pizza
$.75 = the price of a cola
check:
(1) {{{ 3a + 2b = 6 }}}
(1) {{{ 3*1.5 + 2*.75 = 6 }}}
(1) {{{ 4.5 + 1.5 = 6 }}}
(1) {{{ 6 = 6 }}}
OK