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Hanson’s mother loves tea, so Hanson is ordering a custom gift basket of teas for her birthday. He can...

Hanson’s mother loves tea, so Hanson is ordering a custom gift basket of teas for her birthday. He can order up to 120 tea bags to go in the gift basket, and he plans to order a combination of his mother’s two favorites: chamomile and peppermint. The chamomile tea bags each cost $0.50, and the peppermint tea bags each cost $0.40. Hanson is willing to spend up to $55.
Which graph could represent the number of chamomile tea bags, c, and peppermint tea bags, p, that Hanson can order while sticking within his constraints?

Answer

The third graph.

The constraints are c + p ≤ 120, 0.50c + 0.40p ≤ 55, c ≥ 0, and p ≥ 0.

With c on the horizontal axis and p on the vertical axis, the boundary lines are p = 120 − c and p = 137.5 − 1.25c. The correct graph shades the first-quadrant region below both solid lines.

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