Question

Joey has a collection of baseball cards that he has separated into two different value categories. His common cards are worth $0.75 each and his premium cards are worth $2.00 each. Together, Joey’s entire baseball card collection of 88 cards is worth $106.00.

How many cards in Joey’s collection are worth $0.75?

Answer 1

Let x represent the number of $0.75 cards
Let y represent the number of $2 cards
Since he has 88 cards, then
x + y = 88
Now we need an equation that shows the value of the cards.
x number of $0.75 cards are worth 0.75x dollars
y number of $2 cards are worth 2y dollars
The entire collection is worth $106, so
0.75x + 2y = 106

Now we put these two equations together and we have a system of equations that we need to solve.
x + y = 88
0.75x + 2y = 106

Do you know how to solve a system of equations in two variables?