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Emily has some five-dollar bills and some ten-dollar bills. She has 15 bills, and she has 120 dollars. How many five-dollar bills does she have?

You have to yse a table chart

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Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (443 lesson ratings) (443)
1
Let F = The number of $5 bills and T = the number of $10 bills.  She has 15 bills total, so:
 
F+T = 15                
T = 15-F
 
She has $120 total:
 
$120 = ($5)*F + ($10)*T
$120 = $5*F + ($10)*(15-F)         [Substitute 15-F in place of T]
120 = 5F + 150 - 10F
-30 = -5F
 
6 = F
 
Check:
T= 15-F = 15=6 = 9
 
$120 = ($5)*6 + ($10)*9
$120 = $30 + $90
$120 = $120
Check!
Yohan C. | Math Tutor (up to Calculus) (not Statistics and Finite)Math Tutor (up to Calculus) (not Statist...
4.0 4.0 (1 lesson ratings) (1)
0
Hi Malaiyah,
 
Here is how to do it:
 
($10) x + ($5) y = $120
 
x + y = 15
 
x    y
10   5
 
15   0
14   1
13   2
12   3
11   4
10   5
9    6   !
8    7
7    8
6    9
5    10
 
 
First, it has to add up to 15 bills and number of $5 bills must be even because it has to end with 0.  If there are 2 $5 bills, it will add up to $140.  If there are 4 $5 bills, it will add up to $130.  And if there are 6 $5 bills, it will make up $120: $10 x 9 which is $90 and $5 x 6 which is $30.  As you add them together, you will get $120.  There you have it.
 
Good luck.
 
Tip of the day:  Multiples of 5s will only end with 5 or 0.  5 times any odd number will always end with 5 and 5 times any even number will always end with 0.
Francisco P. | Weekend Summer Physics TutorWeekend Summer Physics Tutor
5.0 5.0 (215 lesson ratings) (215)
0
x = $5 dollar bills
 
y = $10 dollar bills
 
x + y = 15
 
5x + 10y = 120
 
Solve for y from the first equation and substitute into the second to get
 
5x + 10(15-x) = 120
 
5x + 150 - 10x = 120
 
-5x = -30
 
x = 6, so y = 9
 
There are six $5 bills and nine $10 bills.