Marta plans to buy a certain number of toothbrushes for a total cost o

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Solution:

To solve this problem, let’s look at the factors of 60 first (since the number of toothbrushes must be a whole number and assume that will be the case for the price of a toothbrush also):

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

We see that 15 is 5 more than 10. So let’s let them be the number of toothbrushes with and without the discount. If she bought 10 toothbrushes for $60 without discount, then each toothbrush costs $6. If she bought 15 toothbrushes for $60 with discount, then each toothbrush costs $4. However, $4 is NOT $1 less than $6.

Next, we see that 20 is also 5 more than 15. So let’s try these two numbers. If she bought 15 toothbrushes for $60 without discount, then each toothbrush costs $4. If she bought 20 toothbrushes for $60 with discount, then each toothbrush costs $3. We see that $3 is exactly $1 less than $4. Therefore, the price of a toothbrush must be $4 before the discount.

Alternate Solution:

Let n be the number of toothbrushes Martha planned to buy. Then, each toothbrush costs 60/n dollars before the discount. With the $1 discount, each toothbrush costs 60/n - 1 dollars and we are told that n + 5 toothbrushes at this price cost $60. We can create the following equation:

(60/n - 1)(n + 5) = 60

60 - n + 300/n - 5 = 60

n + 5 - 300/n = 0

Since n is not zero, we can multiply each side of this equation by n:

n^2 + 5n - 300 = 0

(n - 15)(n + 20) = 0

n = 15 or n = -20

Since the number of toothbrushes cannot be negative, n must be 15. Thus, the price of each toothbrush before the discount is 60/15 = $4.

Answer: C

x = original toothbrush price
N = number of toothbrushes bought

xN = 60

The question says Marta bought 5 more than she intended [N+5] + got a discount $1 on each toothbrush [discount of N+5] + ending up paying the $60 [x(N+5) - (N+5) = 60]

x-----N-----N+5-----x(N+5)-----x(N+5) - (N+5)
2-----30-----35--------70--------------35
3-----20-----25--------75--------------50
4----15----20------80-----------60
5-----12-----17--------85--------------68
6-----10-----15--------90--------------75

Ans: C