Question

There are 21 pieces of $2 notes and $10 notes in an envelope. If the total value of all the notes is less than

$110, find the minimum number of $2 notes in the envelope.

Answer 1

Let the number of $2 notes be x, while that of $10 notes be y.

Set two equations

x + y = 21 y = 21 - x ------- 1

2x + 10y < 110 ------ 2

Sub 1 into 2

2x + 10(21-x) < 110

2x + 210 - 10x < 110

-8x < -100

x > 12.5

Minimum number of $2 notes in the envelope = 13