Question

Jack owns a company which sells handmade greetings cards.

Last year, the company sold 2340 cards and made a total profit of £3510.
This means the average profit per card was £1.50.
This year, Jack is aiming for the company to make 18% more total profit
than last year.
If the average profit per card is 22% lower than last year, how many cards
will Jack's company need to sell this year in order to make their target
profit?

Answer 1

Let the number of cards to be sold this year be x.

The total profit this year can be calculated as:
Total profit = Average profit per card * Number of cards sold

From the given information, we know that:

Last year's profit = £3510
Last year's number of cards sold = 2340
Last year's average profit per card = £1.50
This year's profit target = 18% more than last year's profit = £3510 * 1.18 = £4135.80
This year's average profit per card = 22% lower than last year's average profit per card = £1.50 * 0.78 = £1.17
Using the above information, we can write the equation:
Total profit = Average profit per card * Number of cards sold
£4135.80 = £1.17x

Solving for x, we get:
x = 3540.68

Since we cannot sell a fraction of a card, we need to round up the number of cards to the nearest whole number. Therefore, Jack's company needs to sell at least 3541 cards this year to make their target profit.

Answer 2

Jack's company needs to sell 3540 cards this year in order to make their target profit.

Explanation:

Given the average profit per card last year was £1.50, and the average profit per card is 22% lower this year, this year's average profit per card will be:

`\begin{aligned}\implies \sf Average\;profit\;per\;card&= \£1.50 - (22\% \;\text{of}\; \£1.50)\\&=\£1.50-0.22 * \£1.50\\&=\£1.50-\£0.33\\&=\£1.17\end{aligned}`

Given the total profit Jack is aiming for this year is 18% more than last year's profit of £3510, this year's target profit is:

`\begin{aligned}\implies \sf Target\;profit&=\£3510 + (18\%\;\text{of}\;\£3510)\\&=\£3510 + 0.18 * \£3510\\&=\£3510 + \£631.80\\&=\£4141.80\end{aligned}`

To calculate how many cards Jack's company needs to sell to make this target profit, divide the total target profit by the average profit per card:

`\begin{aligned}\implies \sf Number\;of\;cards&=(4141.80)/(1.17)\\\\&=3540\end{aligned}`

Therefore, Jack's company needs to sell 3540 cards this year in order to make their target profit.