Question

James has a total of 66 dollars in his piggy bank. He only has one dollar bills and two dollar bills in his piggy bank. If there are a total of 49 bills in James's piggy bank, how many one dollar bills does he have?

Answer 1

32 one-dollar bills.

Explanation:

Let x represent one-dollar bills and y represent two-dollar bills.

He has a total of 49 bills. Therefore:

`x+y=49`

The total amount of money James has is 66. x is worth one dollar, while y is worth two dollars. Therefore:

`1x+2y=66\\x+2y=66`

We have a system of equations. Solve by substitution:

`x+2y=66\\x+y=49\\x=49-y\\(49-y)+2y=66\\y=17\\x=49-17=32`

Therefore, James has 32 one-dollar bills and 17 two-dollar bills.

Checking:

`32(1)+17(2)\stackrel{?}{=}66\\32(1)+17(2)\stackrel{\checkmark}{=}66\\\\32+17\stackrel{?}{=}49\\49\stackrel{\checkmark}{=}49`