AMC 10 Step by Step
Log inSign up
Printable

2007 AMC 10A Problem 1

Problem onlyBack to the problem
2007 AMC 10A Problem 1AMC 10 Step by Step
Name:                             Date: September 13, 2026
Ratios, Percents & Averages · difficulty 1 of 5 · about 1 min · position P1-10

One ticket to a show costs $ 20$ at full price. Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickets using a coupon that gives her a 30% discount. How many more dollars does Pam pay than Susan?

  1. A)

    22

  2. B)

    55

  3. C)

    1010

  4. D)

    1515

  5. E)

    2020

Answer

C

Key insight

A 25% discount leaves 75% of the price and a 30% discount leaves 70%; compute each total and subtract.

Solution

A 25%25\% discount means Susan pays 75%75\% of full price on each ticket:
4⋅20⋅0.75=4⋅15=60 dollars.4 \cdot 20 \cdot 0.75 = 4 \cdot 15 = 60 \text{ dollars}.
A 30%30\% discount means Pam pays 70%70\% of full price on each ticket:
5⋅20⋅0.70=5⋅14=70 dollars.5 \cdot 20 \cdot 0.70 = 5 \cdot 14 = 70 \text{ dollars}.
Pam pays 70−60=1070 - 60 = 10 dollars more.

The answer is (C) 10\boxed{\textbf{(C)}\ 10}.

Why this works

A percent discount is a multiplier: "p%p\% off" means multiply by 1−p1001 - \frac{p}{100}. Converting each discount to a per-ticket price (1515 and 1414 dollars) first keeps the arithmetic to small integers and makes the comparison immediate.

The trap

Applying the discount to the ticket count or comparing the discounts themselves instead of the amounts actually paid.

Common mistakes

  • Applying the discount to the ticket count or comparing the discounts themselves instead of the amounts actually paid.
  • Computing the amount saved (2020 and 3030 dollars) and reporting their difference rather than the difference of what was paid.

Techniques

Set up the equation/formula and compute; no special trick needed