William buys a bus ticket every day, Monday to Friday, for $2.50. The bus company has just introduced a card which can be bought to get a discount on all bus fares. Each card is valid for 1 week. William has worked out that he will pay exactly the same amount if he gets the card as he will if he continues to buy tickets at the normal price. Which of the following could be the price and discount for the card?

Explanation

William buys a bus ticket every day from Monday to Friday, so he buys 5 tickets per week. If he continues to buy tickets at the normal price, he will spend:5 tickets/week × $2.50/ticket = $12.50/weekSince William has worked out that he will pay exactly the same amount if he gets the card, we can set up an equation to solve for the cost of the card and the discount on ticket prices:(cost of card) + [(discounted ticket price) × (cost of 5 tickets per week)]Let's try each option:Option A: $5 for the card and a discount of 10% on ticket prices:The cost of the card is $5. The discount on ticket prices is 10%, which reduces the price to $2.25 per ticket.= $5 + ($2.25 x 5) = $16.25/weekOption B: $5 for the card and a discount of 50% on ticket prices:The cost of the card is $5. The discount on ticket prices is 50%, which reduces the price to $1.25 per ticket.= $5 + ($1.25 x 5) = $11.25/weekOption C: $10 for the card and a discount of 50% on ticket prices:The cost of the card is $10. The discount on ticket prices is 50%, which reduces the price to $1.25 per ticket.= $10 + ($1.25 × 5) = $16.25/weekOption D: $10 for the card and a discount of 80% on ticket prices:The cost of the card is $10. The discount on ticket prices is 80%, which reduces the price to $0.50.= $10 + ($0.50 x 5) = $12.50/weekThis is the same as the cost of buying tickets at the normal price, so option D could be correct