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19 votes
19 votes
A stack of 30 bills consists of 1 dollar bills and 5 dollar bills. If the value is $74, how many 1 dollar bills are there?

User Vladimir Arustamian
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1 Answer

25 votes
25 votes

Answer:

19 1-dollar bills

Explanation:

We will call the number of 1 dollar bills "a"

We will call the number of 5 dollar bills "b"

a + b = 30 (the number of 1 dollar bills + the number of 5 dollar bills = 30 bills in total)

1a + 5b = 74 ("a" 1 dollar bills are worth 1a dollars, and "b" 5 dollar bills are worth 5b dollars. In total they are worth 74 dollars)

Next, you can "solve for a variable" in the first equation to plug into the second equation

b = 30 - a (move "a" to the other side, now "b" is equal to 30 - a)

1a + 5(30-a) = 74 (substitute "b" in the second equation for the new value of "b" you found in the previous step)

1a + 150 - 5a = 74 (distribute out 5(30-a) to get 150 - 5a)

-4a = 74 - 150 (combine like terms)

-4a = -76 --> a = 19 (simplify the right side, and divide both sides by -4 to get answer)

Refer back to the first sentence of the explanation where we said the variable "a" equals the number of $1 bills there are. Therefore, there are 19 $1 bills.

User Josh Foskett
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