Question 1203790: Hi
Bob has 3 more $10 notes than $2 notes. The total value of the $2 notes is $94 less than the total value of the $10 notes. How many $2 notes does he have.
Thanks
Found 4 solutions by math_tutor2020, mananth, josgarithmetic, greenestamps:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of $2 notes
x+3 = number of $10 notes
2x = total value of the $2 notes
Example: we have x = 7 of these notes, so 2x = 2*7 = 14 dollars is the subtotal for this category.
10(x+3) = value of the $10 notes only
The phrase "The total value of the $2 notes is $94 less than the total value of the $10 notes" translates to the equation
2x = 10(x+3)-94
Let's isolate x.
2x = 10(x+3)-94
2x = 10x+30-94
2x = 10x-64
2x-10x = -64
-8x = -64
x = -64/(-8)
x = 8
Bob has eight $2 notes
The value so far is 2x = 2*8 = 16 dollars.
Since he has 3 more $10 bills, he would have x+3 = 8+3 = 11 copies of $10 bills
The value here is 10*11 = 110 dollars
Value of the $2 bills: $16
Value of the $10 bills: $110
The gap between these values is $94. This helps confirm we have the right answers.
Another way to verify would be to plug x = 8 into the original equation and simplify both sides.
2x = 10(x+3)-94
2*8 = 10(8+3)-94
2*8 = 10(11)-94
16 = 110-94
16 = 16
Everything works out.
Answer: 8
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! Bob has 3 more $10 notes than $2 notes.
Let number of $2 notes be x
$ 10 notes will be x+3
The total value of the $2 notes is $94 less than the total value of the $10 notes.
$2 notes value = 2x
$10 notes value 10(x+3)
2x = 10(x+3)-94
2x = 10x+30 -94
2x = 10x -64
10x-2x = 64
8x =64
x =8 ---->$2 notes
x+3 = 11 ---> $10 notes
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!
WHICH NOTES QTY. VALUE
$2 x 2x
$10 x+3 10(x+3)
Second sentence in description transcribes to  .
The rest is simple algebra.
.
.
 -------------- 8 of the $2 notes
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You have received three responses showing -- or at least describing -- formal algebraic solutions.
I have a comment regarding those responses.
Look at the sentence that says "The total value of the $2 notes is $94 less than the total value of the $10 notes".
Tutor @josgarithmetic says that translates to the equation  .
Tutor @math_tutor2020 says it translates to 
Although the two equations are equivalent, the second one is FAR better. The first one can teach a student to interpret worded information incorrectly, while the second teaches it correctly. "$94 less than (expression)" means you start with the (expression) and subtract 94. You don't start with the "-94" and add the (expression).
While you should understand how to solve the problem using formal algebra (and even though a formal solution was probably required), you should understand that being able to solve the problem informally using logical reasoning and simple arithmetic gives you valuable problem-solving exercise.
In this problem, you can loan Bob 3 more $2 notes to make the number of $10 and $2 notes equal; the total value of the $2 notes is then only $94-$6 = $88 less than the value of the $10 notes. And since the value of each $2 note is $8 less than the value of each $10 note, the number of notes of each kind he has must be $88/$8 = 11.
Then have Bob give you back the 3 $2 notes you loaned him, leaving him with....
ANSWER: 11-3 = 8 $2 notes (and 11 $10 notes)
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