SOLUTION: Write an equation for these statements 1) Two consecutive integers total thirty-five? 2)The number of moons orbiting Saturn is 18. This is 9 times the number of moons orbitin

Algebra ->  Human-and-algebraic-language -> SOLUTION: Write an equation for these statements 1) Two consecutive integers total thirty-five? 2)The number of moons orbiting Saturn is 18. This is 9 times the number of moons orbitin      Log On


   

Question 1171017: Write an equation for these statements
1) Two consecutive integers total thirty-five?
2)The number of moons orbiting Saturn is 18. This is 9 times the number of moons orbiting Mars.?
3) )The initial letters for the numbers one to ten contain six more consonants than 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
Answer by MathLover1(20849) About Me  (Show Source):
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Write an equation for these statements
1) Two consecutive integers total thirty-five?
let two consecutive integers be x and x%2B1
if total thirty-five, we have
x%2Bx%2B1=35
2x%2B1=35
2x=35-1
2x=34
x=17
and x%2B1=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%2Bv=10
if six more consonants than vowels, we have c=v%2B6
v%2B6%2Bv=10
2v=10-6
2v=4
v=2
c=v%2B6->c=8
there will be 8 consonants and 2vowels
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%2By=2535km.........substitute x
4y%2By=2535km
5y=2535km
y=2535km%2F5
y=507km
then
x=4y....eq.1
x=4%2A507km}
x=2028km}
the flying distance from Toronto to Regina is 2028km
and the flying distance from Toronto to Montreal is 507km