Question

How would you solve the following using a table? Andrew cashes a $ \$180 $ check and wants the money in $ \$10 $ and $ \$20 $ bills. The bank teller gives him $12$ bills. How many of each kind of bill does he receive?

Answer 1

Hint: ere we will assume types of bills “x” and “y” and then will frame the table as per the given data and then simplify it for the resultant required value.

Complete step-by-step answer:
Let us assume the type of bill $ \$10 $ be “x” and
Also assume that the type of bill $ \$20$ be “y”
Now,

Type of bill	No. of Bills	Total Amount
$ \$10 $	X	$10x$
$ \$20 $	Y	$20y$

Now, as we are given that the total amount of $\$ 180$
So, our first equation is –
$10x + 20y = 180$ ….. (A)
Also, we are given that he has received $12$bills in total and therefore, our secondary equation is –
$x + y = 12$
To use the elimination method to get the values of unknown terms one variable from both the equations should be the same. So, multiply the above expression with
$10x + 10y = 120$ ….. (B)
Now, Subtract equation (B) from (A)
$(10x + 20y) - (10x + 10y) = 180 - 120$
When there is a negative sign outside the bracket then the sign of the terms inside the bracket changes. Positive terms become negative and vice-versa.
$10x + 20y - 10x - 10y = 180 - 120$
Like terms with the same value and opposite sign cancel each other.
$ \Rightarrow 10y = 60$
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$ \Rightarrow y = \dfrac{{60}}{{10}}$
Simplify –
$ \Rightarrow y = 6$
Place the above value in the equation -
$x + 6 = 12$
Simplify –
$
   \Rightarrow x = 12 - 6 \\
   \Rightarrow x = 6 \;
 $
Hence, we have six bills each of $ \$10 $ and $ \$20 $.
So, the correct answer is “we have six bills each of $ \$10 $ and $ \$20 $”.

Note: Be careful while framing the equation from the given word problems. Check it twice and be careful while simplifying the mathematical expressions. When you move any term from one side to another then the sign of the terms also changes. Positive term changes to negative and vice-versa.