Answer:
Month since April Number of Ants
0 10,000
1 30,000
2 90,000
3 270,000
4 810,000
Every month, the ant population triples so the multiply the previous population by 3 to find out the new population.
0 months from April = 10,000 * 1 = 10,000 ants
1 month from April = 10,000 * 3 = 30,000 ants
2 months from April = 30,000 * 3 = 90,000 ants
3 months from April = 90,000 * 3 = 270,000 ants
4 months from April = 270,000 * 3 = 810,000
Solve first equation for y:
5x+y=10
y=10-5x. Plug this equation into second equation
-x-(10-5x)=-2
-x-10+5x=-2
4x=8
x=2 (plug x into first equation)
5(2)+y=10
y=0
We need to find the base x in the following equation:

First, lets convert 365 from base 7 to base 10. This is given by

where the upperindex denotes the position of eah number. This gives

that is, 365 based 7 is equal to 194 bases 10.
Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:

where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives

Now, we have all number in base 10. Then, our first equation can be written in base 10 as

For simplicity, we can omit the 10 and get

so, we can solve this equation for x. By combining similar terms. we have

and by moving 197 to the right hand side, we obtain

Finally, we get

Therefore, the solution is x=5
50/2.5=
20
Unit rate is 20 miles per gallon