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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
The hunter should purchase 3 ounces of seeds and 7 ounces of dried fruit to satisfy the scenario.
<u><em>Explanation</em></u>
the amount of seeds and
the amount of dried fruit.
As the hunter needs total 10 ounces of a snack mix , so the first equation will be..
Now the seeds cost $1.50 per ounce and the dried fruit costs $2.50 per ounce. And the mixture costs $2.20 per ounce, so the second equation will be:
According to the substitution method, we will isolate y from the first equation as
Now we will substitute this into the second equation in place of
Plugging this into the equation
, we will get...
So, the hunter should purchase 3 ounces of seeds and 7 ounces of dried fruit to satisfy the scenario.