Mrs seabrooks is buying two types of gifts cards to gives as prizes to employees at a company picnic. She will buy department store gift cards that each cost $50 and coffee shop gift card that each cost $20 .She has $760 to buy a total of 20 gift cards. How many of each type of gift card can Mrs. Seabrooks buy?

Let x equal the number of department store gift cards and let y equal the number of coffee shop gift cards.

We now have two equations making this a linear system of equation

50x + 20y = 760 (the total price of both types of cards purchased)

x + y = 20 (total number of gift cards)

Solve for y for the second equation and you get y = 20 - x.

Substitute this for y into the first equation then solve for x.

50x + 20(20 - x) = 760
50x - 20x + 400 = 760
30x = 360

x = 12 (department store gift cards)

Substitute x into the second equation and solve for y.

12 + y = 20
y = 8 (coffee shop gift cards)

Our final answer is 12 department store gift cards and 8 coffee shop gift cards.