Ms.Erma's oatmeal recipes calls for 2/5 of a cup of raisins.How many batches of cookies can she make if she has 4/5 cup of raisi
1 answer:
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<h2>Greetings!</h2>
<h2>Hope this helps!</h2>
Answer:
It would cost 47.36
Step-by-step explanation:
First, you need to find out how many gallons are needed to fill the tank. To do this, simply multiply 25 by the fraction that is how much is already in there:
25 x = 9.375
So that means that there is 9.375 gallons already in the tank. To find the amount needed to fill the tank:
25 - 9.375 = 15.625
So 15.625 gallons are needed, rounded up to 16 gallons because you cannot get a decimal value of gallons.
That means that 16 x the price = the amount to fill the tank:
16 x 2.96 = 47.36
So it would cost 47.36 to fill the tank!
<h2>Hope this helps!</h2>
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.