Help with compound inequality word problem?

Question

Cara is making a beaded necklace for a gift. She wants to spend between $20 and $30 on the necklace. The bead store charges $2.50 for large beads and $1.25 for small beads. If she buys 3 large beads, how many small beads can she buy to stay within her budget

 

A. Write and solve a compound inequality to describe the range of bead possibilities.

 

B. Answer the question

Answer 1

Let X be the number of small beads:

 

  $20 <  $2.50 * 3 + $1.25 * X <= $30

 

$20 < $7.50 + $1.25* X <= $30

 

12.50 < $1.25*X <= 22.50  <-- subtracts $7.50 from all three sides

 

1250 <= 125X <= 2250 <--- multiplies everything by 100 to clear the decimals

 

10 <= X <= 18  <--- divides everything by 100

 

She can get at least 10 but no more than 18 small beads.