Question

Peter spent half the money on his gift card on

coffee. He loaded another $10 onto the gift card.
How much was on the gift card to begin with if
he now has at least $40 on the card?

Answer 1

There was an initial balance of at least $60 on Peter's gift card.

Explanation:

Inequalities

Is a relation that makes a non-equal comparison between two mathematical expressions. Usual comparators are >, <, ≠, ≤, and ≥.

Let's call x to the original amount Peter had on his gift card balance. We know he spent half of it on coffee. Thus the remaining balance is x/2.

He loaded $10 to his balance, so the new balance is x/2+10. Knowing he now has at least $40, we set the inequality as:

x/2+10 ≥40

Subtracting 10:

x/2 ≥40-10

Operating:

x/2 ≥30

Multiplying by 2:

x≥60

There was an initial balance of at least $60 on Peter's gift card.