**Randall purchased a shirt for $19.44 using a $20 bill. If his correct change was returned in only dimes ($0.10) and pennies ($0.01), how many coins could Randall have received?**

**(A) 9**

**(B) 21**

**(C) 29**

**(D) 37**

**(E) 44**

The solution plugs in different sets of values for dimes and pennies until they get the answer. I found this time-consuming, so is there a way to solve this problem using 2 linear equations?

I tried solving this by taking

**0.1d + 0.01p = 0.56**

**d + p = 0.11**

I’m not sure where I’m going wrong, please help. Thanks in advance!

2nd equation does not hold true as d is a number of dimes and p is a number of pennies.

value of d or value of p must be a positive integer.

apart from equation one, you can add a constraint to the value of 0 < d < 6 and find appropriate pair for the same

hence

0.1d+0.01 p= 0.56 and 0 < d < 6

Now Possible values of pairs are (0,56 ), (1,46), (2,36), (3,26), (4,16), (5,6).

Oh, that makes sense.

Correct me if I’m wrong - You are taking *0 < d < 6* because 1 dime is $0.1 and 6 dimes would be $0.6 which is greater than the change given i.e 0.56?

Yes absolutely correct. I think that’s the easiest way.