Billy has been saving extra money in a jar

Question

Billy has been saving extra money in a jar. He has a mix of one, five, and ten dollar bills. There are 27 bills in the jar for a total of $91 . There are four times as many ones as tens. How many five dollar bills are in the jar?

Answer 1

Let's say x = number of $1 bills, y = number of $5 bills, z = number of $10 bills

eq(1) → x + y + z = 27

eq(2) → x + 5y + 10z = 91

eq(3) → x = 4z

Since equation (3) is in terms of x and z, we need to combine the equations (1) and (2) in such a way that they eliminate y. Let's multiply equation (1) by 5 and subtract equation (2),

5(x + y + z = 27) → 5x + 5y + 5z = 135

5x + 5y + 5z = 135

-(x + 5y + 10z = 91)

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4x - 5z = 44 → eq(4)

Now substitute the value of x in eq(3) into eq(4),

4(4z) - 5z = 44 → 16z - 5z = 44 →11z = 44 → z = 4

Plug value of z into eq(3),

x = 4(4) → x = 16

Plug values for x and z into eq(1)

16 + y + 4 = 27 → 20 + y = 27 → y = 7

Since the problem is asking for the number of $5 bills, and we stated that y = number of $5 bills, our final answer is: There are 7 five dollar bills in the jar.