Question

A student is given the task of buying 100 ballpoint pens with $100. She must buy at least one $10 pen, at least one $3 pen, and the remainder at 50 cents each. How many pens of each kind does she buy?

Answer 1

The correct answer is 5, $10 pens; 1, $3 pen; 94, 50 cents pens.

Explanation:

A student has to buy 100 ball point pens and she has $100 to get the job done.

Price of three different pens are $10, $3 and 50 cents or $0.5.

Let the student buy x number of $10 pens and y number of $3 pens. Number of 50 cents pens bought by the student is 100 - x - y. ( x,y
`\geq` 1)

Total amount spent is 10x + 3y + 0.5(100 - x - y) = 100

⇒ 9.5x + 2.5y + 50 = 100

⇒ 1.9x + 0.5y = 10

⇒ 19x + 5y =100

Value of x (in order to hold the equality where both x and y are positive and greater than 1) is 5 and y is 1.

Total number of 50 cents pen bought is 94.

Thus the student buys 5, $10 pens; 1, $3 pen and 94, 50 cents pens.