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505-555 (Easy)|   Algebra|                           
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woohoo921

Thank you for this explanation. Can you use a combo to solve this problem?

I did 0.1x+.25y=2.35
+ x+y=16
----------------------------------
--> I multiplied the top equation by 100 to get 1-x+25y=235 and the bottom equation by -10 to cancel out the x's to get --> y=5

Your calculations are perfect.
For questions of this nature, we can often use one variable to solve the question or two variables.
Typically, one variable will be faster, but not so much faster that you shouldn't use two variables.
Either works.
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AbdurRakib
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11

As always, if the instinct is to start setting up an algebraic equation, I'd at least consider using PITA (Plug In The Answers). I like testing B and D. B looks easy to work with, so let's start there.
5 25-cent coins and 11 10-cent coins.
5*$0.25 = $1.25
11*$0.10 = $1.10
That's a total of $2.35.
Answer choice B.

If that hadn't worked, we'd have known whether we need a higher value or a lower value. If lower, A would have been right. If higher, we only would have to test D. If D were too high, C is would be the only thing between B and D. If D were too low, we'd know we needed something even higher, so E would be the only option.


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There are two ways to solve questions with systems of two equation non proportional and two variables: substitution or elimination.
This in particular was solved by elimination.
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AbdurRakib
A collection of 16 coins, each with a face value of either 10 cents or 25 cents, has a total face value of $2.35. How many of the coins have a face value of 25 cents?

A) 3
B) 5
C) 7
D) 9
E) 11
We know that number of $0.25 + number of $0.10= 16 and the face value is $2.35
Start with option C [to find whether I should try larger or smaller numbers]
Option C: 7*$0.25= $1.75, which means the other 9 coins are 10 cents; 9*$0.10= $0.90. In total, $1.75+$0.90=$2.65. [ Wrong answer but now I know that the number $0.25 will be less than 7] So try option B
Option B: 5*$0.25= $1.25, which means the other 11 coins are 10 cents; 11*$0.10= $1.10. In total, $1.25+$1.10=$2.35. Right answer.
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