Susan charges twice as much money on credit card with a 7.5% annual interest rate as she does on a card with 6% interest. If her total interest after 1 year is $840, how much did she charge on each card?

credit cards with 7.5% and 6% interest rates? Must be some alternate universe.

Anyway...
amount charged at 6% card --- x
amount charged at other card -- 2x

.06x + .075(2x) = 840
.06x + .15x = 840
.21x=840
x = 4000
She charges $4000 at the 6% card
and $8000 at the 7.5% card

Let's denote the amount Susan charged on the credit card with a 6% interest rate as 'x' dollars.

According to the given information, Susan charges twice as much money on the credit card with a 7.5% interest rate.

Therefore, the amount she charged on the credit card with a 7.5% interest rate is 2x dollars.

Now, let's calculate the interest Susan has to pay for each credit card:

For the credit card with a 6% interest rate:
Interest = Principal × Rate × Time
Interest = x × 6/100 × 1
Interest = 0.06x

For the credit card with a 7.5% interest rate:
Interest = Principal × Rate × Time
Interest = 2x × 7.5/100 × 1
Interest = 0.15x

The total interest she paid after 1 year is $840:

Total Interest = Interest on the 6% card + Interest on the 7.5% card
$840 = 0.06x + 0.15x

Simplifying the equation:
$840 = 0.21x

Dividing both sides of the equation by 0.21:
x = $840 / 0.21
x = $4000

So, Susan charged $4000 on the credit card with a 6% interest rate and $8000 (twice the amount on the 6% card) on the credit card with a 7.5% interest rate.

To solve this problem, let's break it down step by step.

Step 1: Let's assume the amount charged on the card with a 6% interest rate is x dollars.

So, the amount charged on the card with a 7.5% interest rate would be 2x dollars (twice as much as the card with 6% interest).

Step 2: Now, let's calculate the interest on each card using the formula: Interest = Principal * Rate * Time.

For the card with a 6% interest rate, the interest would be: 0.06 * x * 1 (assuming 1 year) = 0.06x.

For the card with a 7.5% interest rate, the interest would be: 0.075 * (2x) * 1 = 0.15x.

Step 3: Since the total interest after 1 year is given as $840, we can set up the equation:

0.06x + 0.15x = 840.

Simplifying the equation, we get: 0.21x = 840.

Step 4: To solve for x, divide both sides of the equation by 0.21:

x = 840 / 0.21.

Performing the calculation, we find: x = 4000.

Step 5: Now that we know the value of x, we can calculate the amount charged on each card:

The amount charged on the card with a 6% interest rate is: x = $4000.

The amount charged on the card with a 7.5% interest rate is: 2x = $8000.

So, Susan charged $4000 on the card with a 6% interest rate and $8000 on the card with a 7.5% interest rate.