Question

In a shop, two kinds of candies A and B were sold at $2 each and $5 each respectively. Tammy paid at least $75 for 20 candies A and B in the shop. Find the maximum number of candy A Tammy bought.

Answer 1

Exact answer not possible: See below.

Explanation:

The total that Tammy would pay is the sum of 2A and 5B, where A and B are the number of candies costing $2 and $5, respectively. Therefore:

2A + 2B = Total Spent

We are told Tammy spent at least $75, which can be written as "Total Spent > $75."

The equation becomes 2A + 5B > 75

Rearranging:

2A + 5B > 75

2A > 75 - 5B

A > (75 - 5B)/2

To find the maximum of the candy A bought, one can try different values of A and B that result in a total of at least $75. If the amount spent were $75 exactly, a solution would be 35 A (for $70), leaving $5 for 1 candy B. But we don't know the exact amount. The problems states "at least $75." As far as we know, Tammy may have spent $105, $405, $1,005, or even $4,005 (200 A and 1 B). One cannot pick a maximum simply since the maximum spent is not defined. The next possible value above $75 would be $77, which represents 36 A and 1 B candies.