Question 1171017

Write an equation for these statements

1) Two consecutive integers total thirty-five?

let two consecutive integers be {{{x}}} and {{{x+1}}}
if total thirty-five, we have
{{{x+x+1=35}}}
{{{2x+1=35}}}
{{{2x=35-1}}}
{{{2x=34}}}
{{{x=17}}}
and {{{x+1=18}}}
two consecutive integers are {{{17}}} and {{{18}}}


2)The number of moons orbiting Saturn is 18. This is 9 times the number of moons orbiting Mars.?
let the number of moons orbiting Saturn be {{{S}}} and
let the number of moons orbiting Mars be {{{M}}}
if the number of moons orbiting Saturn is {{{18}}}, we have {{{S=18}}}
if this is {{{9}}} times the number of moons orbiting Mars, we have
{{{18=9M}}}
{{{2=M}}}
 {{{2}}}  moons orbiting Mars


3)  The initial letters for the numbers one to ten contain six more consonants than vowels.?

there is {{{10}}} letters for  numbers from one to ten

let consonants be {{{c}}} and vowels {{{v}}}
{{{c+v=10}}}
if six more consonants than vowels, we have {{{c=v+6}}}
{{{v+6+v=10}}}
{{{2v=10-6}}}
{{{2v=4}}}
{{{v=2}}}
{{{c=v+6}}}->{{{c=8}}}
there will be {{{8}}} consonants  and {{{2}}}vowels 

4) the flying distance from Toronto to Regina is 4 times the flying distance from Toronto to Montreal. The sum of these distances is 2535km

let the flying distance from Toronto to Regina be {{{x}}}
and the flying distance from Toronto to Montreal be {{{y}}}

if the flying distance from Toronto to Regina is {{{4}}} times the flying distance from Toronto to Montreal, we have

{{{x=4y}}}....eq.1

if the sum of these distances is {{{2535km}}}, we have

{{{x+y=2535km}}}.........substitute {{{x}}}

{{{4y+y=2535km}}}
{{{5y=2535km}}}

{{{y=2535km/5}}}

{{{y=507km}}}

then 

{{{x=4y}}}....eq.1

{{{x=4*507km}}}} 
{{{x=2028km}}}} 

 the flying distance from Toronto to Regina is {{{2028km}}}
and the flying distance from Toronto to Montreal is {{{507km}}}