Question

Select the correct answer.

Kate borrows $200 from her mom to purchase concert tickets in advance to the event. After purchasing the tickets, she saves $20
every two weeks and first uses the money to pay her mom back.
If x is the number of weeks after the concert, and y is the amount of money Kate has, in dollars, which statement is true when the
function values are positive?

Answer 1

Save for 10 weeks then you can pay your mom back

Answer 2

This is a word problem that involves a linear function. A linear function is a function that has a constant rate of change, or slope, and can be written in the form y = mx + b y = m x + b, where m m is the slope and b b is the y-intercept. To solve this problem, we need to find the slope and the y-intercept of the function that models Kate’s situation.

The slope of the function is the rate of change of Kate’s money over time. Since she saves $20 every two weeks, her money increases by $10 every week. Therefore, the slope is 10 10.

The y-intercept of the function is the amount of money Kate has at the start of the time period. Since she borrows $200 from her mom and then pays her back, her initial amount of money is negative 200. Therefore, the y-intercept is -200 -200.

The equation of the function is y = 10x - 200 y = 10 x − 200. This means that for any number of weeks after the concert, x x, Kate’s money, y y, is given by multiplying x x by 10 and subtracting 200.

The question asks which statement is true when the function values are positive. This means that we want to find when y > 0 y > 0. To do this, we can solve for x x in the inequality:

y > 0 10x - 200 > 0 10x > 200 x > 20

This means that Kate’s money is positive when she has saved for more than 20 weeks after the concert. The correct answer is:

Kate has more than $0 after saving for more than 20 weeks after purchasing concert tickets.