An artist sells original hand painted greeting cards. he makes $2.50 profit on a small card and $4.00 profit on a large card. he generally sells 5 large cards for every 2 small cards. he wants to make a profit of $1 from large and small cards this year. find the quantity of each card the artist needs to sell to reach his goal?

Since he sells 5 large cards for every 2 small, we can multiply the number of small cards he needs to sell by 2.5 to find how many large cards he needs to sell.

So let x=the number of small cards sold, and 2.5x=the number of large cards sold

The equation is:Total profit=x+(2.5x)

Since a small card is $2.5, a large card is $4, and the total profit will be $10,000 plug those in to make the equation:

10,000=2.5x+4(2.5x)

We can combine the x's to get 10,000=12.5x and then divide both sides by 12.5 to get x=800.

So he needs to sell 800 small cards.

Multiply that by that 2.5.

And he needs to sell 2000 large cards.