Final answer:
After setting up an equation with the given information and testing each multiple-choice answer, it is found that the correct answer is option (b), where the store sold 112 batteries and 16 boxes of pens.
Step-by-step explanation:
To solve the word problem regarding the sales of batteries and boxes of pens, let's denote the unknown price of a box of pens as 'p' dollars. We are told that 7 times more batteries were sold than boxes of pens, and the total sales were $952.
Let's represent the number of boxes of pens sold as x. Therefore, the number of batteries sold is 7x. Since batteries are sold at $3 each, the total sales from batteries is $3 × 7x, and the total sales from boxes of pens is p × x.
The total sales are given by the equation:
3 × 7x + p × x = $952
This simplifies to:
21x + px = $952
Now, let's check each multiple-choice option by plugging in the values for the number of batteries (7x) and boxes of pens (x):
- For option (a), if 15 boxes of pens were sold, then 104 batteries were sold (7 × 15). Plug in x = 15 into the equation: 21 × 15 + 15p = $952. This gives us 315 + 15p = $952.
- For option (b), if 16 boxes of pens were sold, then 112 batteries were sold (7 × 16). Plug in x = 16 into the equation: 21 × 16 + 16p = $952. This gives us 336 + 16p = $952.
- For option (c), if 17 boxes of pens were sold, then 120 batteries were sold (7 × 17). Plug in x = 17 into the equation: 21 × 17 + 17p = $952. This gives us 357 + 17p = $952.
- For option (d), if 18 boxes of pens were sold, then 128 batteries were sold (7 × 18). Plug in x = 18 into the equation: 21 × 18 + 18p = $952. This gives us 378 + 18p = $952.
Upon solving each equation, only option (b) results in a whole number price for a box of pens, which makes it the correct answer. Therefore, the store sold 112 batteries and 16 boxes of pens.