Mrs. James is makes scarves. She has 21 2/3
1 answer:
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Let's call the two numbers and
.
Given these variables, we can say: , based on the first sentence in the problem.
Also, remember that the reciprocal of a number is simply 1 divided by the number. Thus, we can say that:
To solve, we can simply substitute in for
in the second equation and solve.
- Set up
- Get terms on the left side to a common denominator for easier addition
- Simplify
- Cross multiplication (
)
- Simplify
- Subtract
from both sides of the equation
- Factor left side of the equation
- Zero Product Property
Now, notice that we have found two solutions, but the problem is only asking for one. This <em>likely </em>means that one of our solutions is extraneous. Let's take a look. Remember that the smaller positive number is equal to 14 less than the larger number. However,
,
Since is not positive in this case,
is not a solution.
Thus, is our only solution. In this case,
,
which means that the smaller number is 14 and the larger number is 28.
We can rewrite the expression under the radical as
then taking the fourth root, we get
Why the absolute value? It's for the same reason that
since both and
return the same number
, and
captures both possibilities. From here, we have
The absolute values disappear on all but the term because all of
,
and
are positive, while
could potentially be negative. So we end up with
The answer is 8
Here's why:
The exponents are subtracted one from another when divided.
We can look at the problem this way:
Since we have the power of -1 on the 3, we apply this rule:
Also this rule because we have the power of 1 on the 6:
Then we get this:
We apply the rule:
We get this:
Here's why:
The exponents are subtracted one from another when divided.
We can look at the problem this way:
Since we have the power of -1 on the 3, we apply this rule:
Also this rule because we have the power of 1 on the 6:
Then we get this:
We apply the rule:
We get this: