Question

Harvey has some $1 and some$5 bills. in all, has 6 bills worth $22. let x be the number of $1 bills and let y be the number $5 bills. write a system of equations to represents the information and use substitution to determine how many bills of each denomination harvey has

Answer 1

x+y=22

(4,2)

x     y

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Answer 2

The system of equations that represents the information is:

$x + y = 6\\x + 5y =22$

Harvey has got 2 bills of $1 and 4 bills of $5

Given that:

• Harvey has got x numbers of $1 bills

• She has got y numbers of $5 bills

• Total amount she has = $22

• Total bills she got =  6

Calculations and formation of equations:

Total bills = $1 bills + $2 bills

$6 = x + y$

Total amount she got = amount by $1 bills + amount by $5 bills

$\ 22 = x \times \ 1 + y \times \ 5\\22 = x + 5y$

Thus, the system of equations she got are:

$x + y = 6\\x + 5y =22$

Using substitution method for finding the values of x and y:

From first equation we have:

$x + y = 6\\x = 6 -y$

Substituting this value of x in second equation:

$6-y + 5y = 22\\\\4y = 22 - 6\\\\y = \dfrac{16}{4}\\\\y = 4$

Thus x = 6 - y = 6 - 4 = 2

Thus, Harvey has got 2 bills of $1 and 4 bills of $5

Learn more about system of equations here:

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