Question

charlie pays $29.75 for 12 pens and 7 pencils. if a pen costs $0.50 more than a pencil, how much will his friend pay for 15 pens and 4 pencils? $25.75 $38.50 $31.25 $41.25

Explanation:

Step1: Define variables

Let the cost of a pencil be $x$. Then the cost of a pen is $(x + 0.50)$.

Step2: Set up the equation

The total cost for 12 pens and 7 pencils is $29.75$. So, $12(x + 0.50) + 7x = 29.75$.

Step3: Solve the equation

First, expand the left side: $12x + 6 + 7x = 29.75$.
Combine like terms: $19x + 6 = 29.75$.
Subtract 6 from both sides: $19x = 29.75 - 6 = 23.75$.
Divide both sides by 19: $x = \frac{23.75}{19} = 1.25$.
So, a pencil costs $1.25, and a pen costs $1.25 + $0.50 = $1.75.

Step4: Calculate the cost for 15 pens and 4 pencils

The cost for 15 pens is $15 \times 1.75 = 26.25$.
The cost for 4 pencils is $4 \times 1.25 = 5$.
Total cost: $26.25 + 5 = 31.25$.

Answer:

$31.25$ (corresponding to the option \$31.25)