Question

dan recently received his first credit card, a mastercard with a credit line of $500. in the first month he had it, he ran up charges of $425. how much of that must he pay if he wants to charge a discount airline ticket, which costs $200, on his card without going over his credit limit?

credit line......................$1,000.00
credit available................$ 150.00

a. all of it
b. $175
c. $75
d. $125

Explanation:

Step1: Determine remaining credit needed

The airline - ticket costs $200 and the current available credit is $150. We need to find out how much more credit is needed. Let $x$ be the amount to be paid.
We know that the amount to be paid will increase the available credit.

Step2: Set up the equation

The amount of credit we need to add to the current available credit ($150$) to be able to charge the $200$ - dollar ticket is given by the equation $x+150 = 200$.

Step3: Solve for $x$

Subtract $150$ from both sides of the equation: $x=200 - 150$.
$x = 50$. But this is wrong. Let's start over.

The credit - line is $1000$. The current charges are $425$ and the ticket costs $200$. The total amount if no payment is made is $425 + 200=625$.
We want to stay within the credit - line of $1000$. Let the amount to be paid be $y$.
The equation is $(425 - y)+200\leq1000$. We want to find the minimum $y$ such that we don't go over the limit.
We can also think of it in terms of available credit. The available credit is currently $1000 - 425 = 575$.
We need to have at least $200$ available credit. Let the amount to be paid be $a$.
The current available credit is $1000 - 425=575$. After paying $a$ dollars, the new available credit should be enough for the $200$ - dollar ticket.
The new available credit is $(1000 - 425 + a)$. We want $(1000 - 425 + a)\geq200$.
We know that the amount of money we need to free up is $200-(1000 - 425)=200 - 575=- 375$ (wrong approach).

The correct way:
The credit line is $1000$. The current charges are $425$ and we want to add a $200$ charge. So the total we would have is $425 + 200=625$.
To stay within the $1000$ credit - line, we note that the current available credit is $1000 - 425 = 575$.
We need to pay enough so that we can charge the $200$ - dollar ticket.
Let the amount to be paid be $p$.
We know that the amount of credit we need to free up is $200-(1000 - 425)$.
The amount we need to pay is $425+200 - 1000+425$.
The amount of credit we need to make available for the $200$ - dollar ticket:
The current charges are $425$. The credit line is $1000$.
We want to charge a $200$ - dollar ticket.
Let the amount to be paid be $x$.
The available credit after paying $x$ dollars is $(1000-(425 - x))$. We want $(1000-(425 - x))\geq200$.
Simplifying, $1000 - 425+x\geq200$, $575+x\geq200$, $x\geq200 - 575$ (wrong).

The correct approach:
The credit line is $1000$. The current charges are $425$. We want to charge a $200$ - dollar ticket.
The total amount of charges we want to have is $425+200$. But we can't go over $1000$.
Let the amount to be paid be $y$.
We know that $425 - y+200\leq1000$.
We want to find the minimum $y$ such that the inequality holds.
The current available credit is $1000 - 425 = 575$.
We need $200$ available credit for the ticket.
The amount we need to pay is $425-(1000 - 200)=425 - 800=-375$ (wrong).

The correct way:
The credit line is $1000$.
The current charge is $425$ and the new charge is $200$.
The total charge without payment is $425 + 200=625$.
To stay within the credit - line, we need to pay enough so that the total charge is at most $1000$.
The amount we need to pay is $(425 + 200)-1000 + 425=125$.

Answer:

D. $125$