Question 912241

let's cars be {{{x}}} and buses {{{y}}}

given: {{{x+y=7}}} ...eq.1

 {{{195}}} students went on a field trip 
each car holds {{{5}}} students and each bus hold {{{45}}} students

 {{{5x+45y=195}}}  ....eq.2

solve the system:

{{{x+y=7}}} ...eq.1
{{{5x+45y=195}}}  ....eq.2
___________________________

{{{x+y=7}}} ...eq.1 ...solve for {{{x}}}

{{{x=7-y}}} ...substitute in eq.2


{{{5x+45y=195}}}  ....eq.2

{{{5(7-y)+45y=195}}}  ...solve for {{{y}}}

{{{35-5y+45y=195}}}

{{{-5y+45y=195-35}}}

{{{40y=160}}}

{{{y=160/40}}}

{{{highlight(y=4)}}}

find {{{x}}}

{{{x=7-y}}}

{{{x=7-4}}}

{{{highlight(x=3)}}}

so, the number of cars is {{{highlight(x=3)}}}  and the number of buses is {{{highlight(y=4)}}}

check:

{{{5x+45y=195}}}  ....eq.2

{{{5*3+45*4=195}}}  

{{{15+180=195}}} 

{{{195=195}}}