A shop sells gift wrap for $4 per package and greeting cards for $10 per package. If the shop

sells 205 packages in all and receives a total of $1084, how many packages of gift wrap and

greeting cards were sold?

Total number of gift wraps sold = 161

The number of cards sold = 44

Step-by-step explanation:

Selling price of each gift wrap = $4

Selling price of each greeting card = $10

Total packages sold by the shop = 205

Total amount earned = $1084

Now, let the number of gift wraps sold = m

⇒ The cost of m gift wraps = m x Cost of each gift wrap

= m x ($4) = 4 m

Also, the number of greetings cards sold = (205 - m)

⇒ The cost of (205-m) greetings cards

= (205-m) x Cost of each greetings cards

= (205-m) x $10 = $2050 - 10 m

According to the question,

Total earned amount = Amount earned from Gift wrap + Greeting cards

or, $1084 = 4 m + ($2050 - 10m)

or, 1084 - 2050 = 4 m - 10 m

⇒ - 6 m = - 966

or, m = 966 / 6 = 161

Hence, the total number of gift wraps sold = m = 161

And, the number of cards sold = 205 - m = 205 - 161 = 44