Question

1. maria bought 2 notebooks and 3 folders for $7.35. her friend bought 4 notebooks and 2 folders for $9.40. how much does each notebook and folder cost?

Explanation:

Step1: Define variables

Let $n$ = cost of 1 notebook, $f$ = cost of 1 folder.

Step2: Set up equations

Maria's purchase: $2n + 3f = 7.35$
Friend's purchase: $4n + 2f = 9.40$

Step3: Eliminate $n$ variable

Multiply first equation by 2: $4n + 6f = 14.70$
Subtract second equation:
$$(4n + 6f) - (4n + 2f) = 14.70 - 9.40$$
$$4f = 5.30$$

Step4: Solve for $f$

$$f = \frac{5.30}{4} = 1.325$$

Step5: Solve for $n$

Substitute $f=1.325$ into $2n + 3f = 7.35$:
$$2n + 3(1.325) = 7.35$$
$$2n + 3.975 = 7.35$$
$$2n = 7.35 - 3.975 = 3.375$$
$$n = \frac{3.375}{2} = 1.6875$$

Answer:

Each notebook costs $\$1.69$ (rounded to the nearest cent) and each folder costs $\$1.33$ (rounded to the nearest cent).
Or as exact values: Notebook: $\$1.6875$, Folder: $\$1.325$