Question

A college radio station sponsors a contest once a week. One resident from a dormitory calls in and tries to answer ten questions correctly. Each correct answer earns the dorm $50, but each incorrect answer reduces the winnings by $25. Last week’s contestant earned $350. How many answers were correct?​

Answer 1

Answer:

There were 8 correct answers and 2 incorrect answers.

Step-by-step explanation:

The contest consists of paying $50 for each correctly answered question and subtracting $25 for each incorrectly answered question.

Let's call:

x = Number of correct answers

y = Number of incorrect answers

The resident from a dormitory answered 10 questions last week. This leads to the following condition:

$x + y = 10\qquad\qquad [1]$

Since each correct answer adds $50 and each incorrect answer subtracts $25, the weekly balance is

50x - 25y

The contestant earned $350, thus:

50x - 25y = 350

Dividing by 25:

2x - y = 14

Adding this equation with [1]:

x + 2x = 24

Simplifying:

3x = 24

x = 24 / 3

x = 8

From [1]:

y = 10 - x = 10 - 8

y = 2

There were 8 correct answers and 2 incorrect answers.