Question

work space for problem 2
bri bought a total of 12 items from the book store.
each item was either a pack of pencils of $1.25 or a
spiral notebook for $3.50.
she spent a total of $37.50.
how many packs of pencils did she buy?

Explanation:

Step1: Define variables

Let \( x \) be the number of pencil packs and \( y \) be the number of notebooks. We know two equations: \( x + y = 12 \) (total items) and \( 1.25x + 3.50y = 37.50 \) (total cost).

Step2: Solve the system of equations

From the first equation, we get \( y = 12 - x \). Substitute this into the second equation:
\( 1.25x + 3.50(12 - x) = 37.50 \)
Expand: \( 1.25x + 42 - 3.50x = 37.50 \)
Combine like terms: \( -2.25x + 42 = 37.50 \)
Subtract 42: \( -2.25x = -4.50 \)
Divide by -2.25: \( x = \frac{-4.50}{-2.25} = 2 \)? Wait, no, wait—wait, let's check again. Wait, 3.5012 is 42, 42 - 37.50 is 4.50, so -2.25x = -4.50, so x = 2? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, let's re - calculate. Wait, 1.25x + 3.5y = 37.5, y = 12 - x. So 1.25x + 3.5(12 - x)=37.5. 3.512 = 42, so 1.25x + 42 - 3.5x = 37.5. 1.25x - 3.5x = -2.25x. 42 - 37.5 = 4.5. So -2.25x = -4.5. Then x = (-4.5)/(-2.25)=2? Wait, but that seems low. Wait, maybe the cost of notebooks is $3.50, pencils $1.25. Wait, maybe I mixed up. Wait, no, the problem says "each item was either a pack of pencils for $1.25 or a spiral notebook for $3.50". So total items 12, total cost 37.50. Wait, maybe my variable definition is wrong. Wait, no, x is pencil packs, y is notebooks. Wait, let's check with x = 10. Wait, no, let's do the math again. Wait, -2.25x = -4.5, so x = 2? But if x = 2, then y = 10. Then total cost is 21.25 + 103.50 = 2.5 + 35 = 37.5. Oh! Right, that works. So x = 2? Wait, no, 2 packs of pencils and 10 notebooks. Wait, but the question is "how many packs of pencils did she buy?" So x = 2? Wait, but let's check again. 21.25 = 2.5, 103.5 = 35, 2.5+35 = 37.5. Yes, that's correct. Wait, so the number of pencil packs is 2? Wait, but that seems like a small number, but the math checks out.

Answer:

2