Question 373744
Let {{{c}}} = number of cats
Let {{{d}}} = number of dogs
given:
(1) {{{c + d = 34}}}
In 1 day, {{{c}}} cats eat {{{.5c}}} cans of food
In 1 day {{{d}}} dogs eat {{{1.5d}}} cans of food
(2) {{{.5c + 1.5d = 36}}}
(2) {{{5c + 15d = 360}}}
Multiply both sides of (1) by {{{5}}}
and subtract from (2)
(2) {{{5c + 15d = 360}}}
(1) {{{-5c - 5d = 170}}}
{{{10d = 190}}}
{{{d = 19}}}
And, since
(1) {{{c + d = 34}}}
{{{c + 19 = 34}}}
{{{c = 15}}}
Ther are 15 cats and 19 dogs