Hi Amy!
Let's walk through this math word problem together.
You have two kinds of bills: one dollar and ten dollar
there are a total of 52 bills: number of one dollar bills + number of ten dollar bills = 52
Now let's look at the value of the bills: $1.00 bills + $10.00 bills = $196.00
What you have are two equations. number of one dollar bills + number of ten dollar bills = 52
number of $1.00 bills + number of $10.00 bills = $196.00
Let n = number of one dollar bills
Let t = number of ten dollar bills
So we have: n + t =52
$1.00n + $10.00t = $196.00
With these two equations, we have a system of equations. The coefficient of n and t is 1. Subtracting the two equations, we can solve for t.
n + t = 52
(-) 1.00n + 10.00t = 196.00
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(n - 1.00n) + (t - 10.00t) = (52 - 196.00)
0 + -9.00t = -144
t = -144/-9.00
t = 16
Since t = 16 the number of $10 bills, we can use the first equation to find the number of $1.00 bills.
n + t = 52
n + 16 = 52
n 16 -16 = 52 -16
n = 36
Your answer is: There are 16 ten dollar bills and 36 one dollar bills.
BUT, you should always CHECK your answer. You can do that by substitution the found values into the second equation.
$1.00n + $10.00t = $196.00
$1.00(36) + $10.00(16) = $196.00
$36.00 + $160.00 = $196.00
$196.00 = $196.00 IT CHECKS!!
I hope you have a better understanding of the process now.
THINK MATH!!!
