Question

3 pens and 3 notebooks cost $13.50 while 4 pens and 14 notebooks costs $51.00. let x and y be the prices of a pen and a notebook respectively. equation 1: 3x + 3y = 13.50 equation 2: 4x + 14y = 51.00 11a select the correct price of a pen and a notebook. x = 1.20, y = 3.30 (a) x = 2.00, y = 7.00 (b) x = 1.00, y = 1.00 (c) x = 1.65, y = 0.60 (d)

Explanation:

Step1: Simplify Equation 1

Divide Equation 1 ($3x + 3y = 13.50$) by 3: $x + y = 4.50$, so $x = 4.50 - y$.

Step2: Substitute into Equation 2

Substitute $x = 4.50 - y$ into Equation 2 ($4x + 14y = 51.00$):
$4(4.50 - y) + 14y = 51.00$
$18 - 4y + 14y = 51.00$
$10y = 33.00$
$y = 3.30$

Step3: Find x

Substitute $y = 3.30$ into $x = 4.50 - y$:
$x = 4.50 - 3.30 = 1.20$

Answer:

A. \( x = 1.20 \), \( y = 3.30 \)