Andrea has some money. Her brother gives her 7 coins worth 23 cents and now she has 73 cents. If she started with 5 coins, what
1 answer:
Andrea had 5 coins worth 50 cents ! And , thereafter her brother gave her 7 coins worth 23 cents .
<u>Step-by-step explanation:</u>
Here we have , Andrea has some money. Her brother gives her 7 coins worth 23 cents and now she has 73 cents. If she started with 5 coins, We need to find what coins did Andrea's brother give her and what coins did Andrea start with. Let's find out:
Andrea has some money , and her brother gives her 7 coins ! worth 23 cents . So , 1 coin worth is :
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Now , she had a total of 73 cents i.e.
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Initially Andrea had 5 coins worth 50 cents ! And , thereafter her brother gave her 7 coins worth 23 cents .
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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.