Question

Jenny is going to design and sell digital greeting cards through CelebrationStock. The online

platform informs Jenny that, based on market research, she will sell -15x + 120 cards in her
first month if she charges x dollars per card.
CelebrationStock will charge Jenny 30% of the amount she charges per card. So, Jenny will
earn 70% of the amount she charges per card, or 0.7x dollars, in profit.
To the nearest dollar, what is the highest price Jenny can charge per card to earn $125 in
profit in her first month?

Answer 1

Jenny can charge approximately $8 per card to reach her profit goal of $125 in her first month, assuming she sells -15x + 120 cards when charging x dollars per card and retains 70% of the card price as profit.

Step-by-step explanation:

We need to find the highest price x that Jenny can charge for her digital greeting cards to earn $125 in profit in her first month. The profit formula given is -15x + 120 for the number of cards sold, and Jenny earns 70% of the price per card, or 0.7x dollars in profit per card.

First, let's find the total profit equation by multiplying the number of cards sold by Jenny's earnings per card, which is (-15x + 120) × 0.7x. We then set this equation equal to the desired profit of $125:

(-15x + 120) × 0.7x = 125

Now, we expand and simplify the equation to solve for x:

-10.5x² + 84x = 125

Moving 125 to the left side and simplifying, we get:

-10.5x² + 84x - 125 = 0

To solve the quadratic equation, we can use the quadratic formula:

x = [-84 ± √((84²) - 4(-10.5)(-125))]/(2(-10.5))

Calculating the discriminant and then the roots, we find the maximum price Jenny can charge per card. Since the price must be non-negative, we take the positive root of the equation. After calculating, we find that the highest price rounded to the nearest dollar is approximately $8 per card for Jenny to reach her profit goal.

Answer 2

6

Step-by-step explanation:

To find the highest price Jenny can charge to earn $125 in profit, first write an equation.

total profit = profit per card * number of cards

You want to know when Jenny will earn $125 in profit, and the price per card, x, is the variable. The expression 0.7x represents the profit per card.

125=0.7x(–15x+120)

Now, solve for x. Start by writing the equation in standard form

125=0.7x(–15x+120)

125= –10.5x2+84x

0= –10.5x2+84x–125

Now to solve for x, you can use the quadratic formula with a= – 10.5, b=84, and

So, to the nearest dollar, the highest price Jenny can charge per card to earn $125 in profit is $6.0236 or $6.