Question

Mrs. Cho is bringing cans and bottles to a recycling center. For a type A can, she gets 5 cents. For type B can, she gets 10 cents. She knows that she has redeemed at least 11 cans but has no more than 95cents. What are the possible combinations?

Answer 1

One possible solution be -

Mrs. Cho is brings type A cans = 10

Mrs. Cho is brings type B cans = 3

Explanation:

Let us assume

Mrs. Cho is brings type A cans = x

Mrs. Cho is brings type B cans = y

As given,

For a type A can, she gets 5 cents and For type B can, she gets 10 cents

As we have x Type A cans and y Type B cans

And she has redeemed no more than 95 cents

⇒5x + 10y ≤ 95 .......(1)

Also given,

She has redeemed at least 11 cans

⇒ x + y ≥ 11 ........(2)

∴ we get

x + y ≥ 11

5x + 10y ≤ 95

By applying graphical method , we get

The equations become

5x + 10y = 95 .......(1)

x + y = 11 ........(2)

Table for equation (1) -

x y

0 9.5

19 0

Table for equation (2) -

x y

0 11

11 0

The two lines intersect at point (3, 8)

So the possible combinations are in the shaded portion which is covered by both the lines.

One possible combination is ( 10, 3) which lies in the shaded region.

So,

Mrs. Cho is brings type A cans = x = 10

Mrs. Cho is brings type B cans = y = 3