Which equation can be used to find two numbers such that twice the first equals three times the second and three times their dif
ference exceeds twice their difference by 13?
1 answer:
Let the numbers be a and b and b>a
2a=3b and 3(b-a)=2(b-a)+13
Solving the first for a:
2a=3b
a=3b/2, now using this value of a in the second equation gives you:
3(b-3b/2)=2(b-3b/2)+13 upon performing indicated operations.
3b-9b/2=2b-6b/2+13 making all terms have a common denominator of 2
(6b-9b)/2=(4b-6b+26)/2 multiplying the whole equation by 2
6b-9b=4b-6b+26 combining like terms
-3b=-2b+26 adding 2b to both sides
-b=26 dividing both sides by -1
b=-26, since a=3b/2
a=3(-26)/2
a=-39
So the numbers are -39 and -26
check...
2a=3b becomes:
2(-39)=3(-26)
-78=-78
3(b-a)=2(b-a)+13 becomes:
3(-26--39)=2(-26--39)+13
3(13)=2(13)+13
39=26+13
39=39
correct :P
You might be interested in
The answer is 11 for this question
let the number be xy then
x + y = 12
y - x = 2 ( because y > x)
adding we get 2y = 14 so y = 7
and x = 12 - 7 = 5
So the number is 57.
For 16 it's 8/10 for 17 it's 52/100 for 18 it's -92/100 for 19 it's -48/100 for 20 it's 86/100 for 21 it's 76/100
2.625 gallons a day
14 oz x 24 hours = 336 oz per day
336 oz converted to gallons is 2.625 gallons